---
_id: '14427'
abstract:
- lang: eng
text: In the paper, we establish Squash Rigidity Theorem—the dynamical spectral
rigidity for piecewise analytic Bunimovich squash-type stadia whose convex arcs
are homothetic. We also establish Stadium Rigidity Theorem—the dynamical spectral
rigidity for piecewise analytic Bunimovich stadia whose flat boundaries are a
priori fixed. In addition, for smooth Bunimovich squash-type stadia we compute
the Lyapunov exponents along the maximal period two orbit, as well as the value
of the Peierls’ Barrier function from the maximal marked length spectrum associated
to the rotation number 2n/4n+1.
acknowledgement: 'VK acknowledges a partial support by the NSF grant DMS-1402164 and
ERC Grant #885707. Discussions with Martin Leguil and Jacopo De Simoi were very
useful. JC visited the University of Maryland and thanks for the hospitality. Also,
JC was partially supported by the National Key Research and Development Program
of China (No.2022YFA1005802), the NSFC Grant 12001392 and NSF of Jiangsu BK20200850.
H.-K. Zhang is partially supported by the National Science Foundation (DMS-2220211),
as well as Simons Foundation Collaboration Grants for Mathematicians (706383).'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jianyu
full_name: Chen, Jianyu
last_name: Chen
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Hong Kun
full_name: Zhang, Hong Kun
last_name: Zhang
citation:
ama: Chen J, Kaloshin V, Zhang HK. Length spectrum rigidity for piecewise analytic
Bunimovich billiards. Communications in Mathematical Physics. 2023. doi:10.1007/s00220-023-04837-z
apa: Chen, J., Kaloshin, V., & Zhang, H. K. (2023). Length spectrum rigidity
for piecewise analytic Bunimovich billiards. Communications in Mathematical
Physics. Springer Nature. https://doi.org/10.1007/s00220-023-04837-z
chicago: Chen, Jianyu, Vadim Kaloshin, and Hong Kun Zhang. “Length Spectrum Rigidity
for Piecewise Analytic Bunimovich Billiards.” Communications in Mathematical
Physics. Springer Nature, 2023. https://doi.org/10.1007/s00220-023-04837-z.
ieee: J. Chen, V. Kaloshin, and H. K. Zhang, “Length spectrum rigidity for piecewise
analytic Bunimovich billiards,” Communications in Mathematical Physics.
Springer Nature, 2023.
ista: Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise
analytic Bunimovich billiards. Communications in Mathematical Physics.
mla: Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich
Billiards.” Communications in Mathematical Physics, Springer Nature, 2023,
doi:10.1007/s00220-023-04837-z.
short: J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics
(2023).
date_created: 2023-10-15T22:01:11Z
date_published: 2023-09-29T00:00:00Z
date_updated: 2023-12-13T13:02:44Z
day: '29'
department:
- _id: VaKa
doi: 10.1007/s00220-023-04837-z
ec_funded: 1
external_id:
arxiv:
- '1902.07330'
isi:
- '001073177200001'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.07330
month: '09'
oa: 1
oa_version: Preprint
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Length spectrum rigidity for piecewise analytic Bunimovich billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2023'
...
---
_id: '12877'
abstract:
- lang: eng
text: We consider billiards obtained by removing from the plane finitely many strictly
convex analytic obstacles satisfying the non-eclipse condition. The restriction
of the dynamics to the set of non-escaping orbits is conjugated to a subshift,
which provides a natural labeling of periodic orbits. We show that under suitable
symmetry and genericity assumptions, the Marked Length Spectrum determines the
geometry of the billiard table.
acknowledgement: 'J.D.S. and M.L. have been partially supported by the NSERC Discovery
grant, reference number 502617-2017. M.L. was also supported by the ERC project
692925 NUHGD of Sylvain Crovisier, by the ANR AAPG 2021 PRC CoSyDy: Conformally
symplectic dynamics, beyond symplectic dynamics (ANR-CE40-0014), and by the ANR
JCJC PADAWAN: Parabolic dynamics, bifurcations and wandering domains (ANR-21-CE40-0012).
V.K. acknowledges partial support of the NSF grant DMS-1402164 and ERC Grant # 885707.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jacopo
full_name: De Simoi, Jacopo
last_name: De Simoi
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Martin
full_name: Leguil, Martin
last_name: Leguil
citation:
ama: De Simoi J, Kaloshin V, Leguil M. Marked Length Spectral determination of analytic
chaotic billiards with axial symmetries. Inventiones Mathematicae. 2023;233:829-901.
doi:10.1007/s00222-023-01191-8
apa: De Simoi, J., Kaloshin, V., & Leguil, M. (2023). Marked Length Spectral
determination of analytic chaotic billiards with axial symmetries. Inventiones
Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-023-01191-8
chicago: De Simoi, Jacopo, Vadim Kaloshin, and Martin Leguil. “Marked Length Spectral
Determination of Analytic Chaotic Billiards with Axial Symmetries.” Inventiones
Mathematicae. Springer Nature, 2023. https://doi.org/10.1007/s00222-023-01191-8.
ieee: J. De Simoi, V. Kaloshin, and M. Leguil, “Marked Length Spectral determination
of analytic chaotic billiards with axial symmetries,” Inventiones Mathematicae,
vol. 233. Springer Nature, pp. 829–901, 2023.
ista: De Simoi J, Kaloshin V, Leguil M. 2023. Marked Length Spectral determination
of analytic chaotic billiards with axial symmetries. Inventiones Mathematicae.
233, 829–901.
mla: De Simoi, Jacopo, et al. “Marked Length Spectral Determination of Analytic
Chaotic Billiards with Axial Symmetries.” Inventiones Mathematicae, vol.
233, Springer Nature, 2023, pp. 829–901, doi:10.1007/s00222-023-01191-8.
short: J. De Simoi, V. Kaloshin, M. Leguil, Inventiones Mathematicae 233 (2023)
829–901.
date_created: 2023-04-30T22:01:05Z
date_published: 2023-08-01T00:00:00Z
date_updated: 2023-10-04T11:25:37Z
day: '01'
department:
- _id: VaKa
doi: 10.1007/s00222-023-01191-8
ec_funded: 1
external_id:
arxiv:
- '1905.00890'
isi:
- '000978887600001'
intvolume: ' 233'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.1905.00890
month: '08'
oa: 1
oa_version: Preprint
page: 829-901
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Inventiones Mathematicae
publication_identifier:
eissn:
- 1432-1297
issn:
- 0020-9910
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Marked Length Spectral determination of analytic chaotic billiards with axial
symmetries
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 233
year: '2023'
...
---
_id: '12145'
abstract:
- lang: eng
text: In the class of strictly convex smooth boundaries each of which has no strip
around its boundary foliated by invariant curves, we prove that the Taylor coefficients
of the “normalized” Mather’s β-function are invariant under C∞-conjugacies. In
contrast, we prove that any two elliptic billiard maps are C0-conjugate near their
respective boundaries, and C∞-conjugate, near the boundary and away from a line
passing through the center of the underlying ellipse. We also prove that, if the
billiard maps corresponding to two ellipses are topologically conjugate, then
the two ellipses are similar.
acknowledgement: "We are grateful to the anonymous referees for their careful reading
and valuable remarks and\r\ncomments which helped to improve the paper significantly.
We gratefully acknowledge support from the European Research Council (ERC) through
the Advanced Grant “SPERIG” (#885707)."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Edmond
full_name: Koudjinan, Edmond
id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E
last_name: Koudjinan
orcid: 0000-0003-2640-4049
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Koudjinan E, Kaloshin V. On some invariants of Birkhoff billiards under conjugacy.
Regular and Chaotic Dynamics. 2022;27(6):525-537. doi:10.1134/S1560354722050021
apa: Koudjinan, E., & Kaloshin, V. (2022). On some invariants of Birkhoff billiards
under conjugacy. Regular and Chaotic Dynamics. Springer Nature. https://doi.org/10.1134/S1560354722050021
chicago: Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff
Billiards under Conjugacy.” Regular and Chaotic Dynamics. Springer Nature,
2022. https://doi.org/10.1134/S1560354722050021.
ieee: E. Koudjinan and V. Kaloshin, “On some invariants of Birkhoff billiards under
conjugacy,” Regular and Chaotic Dynamics, vol. 27, no. 6. Springer Nature,
pp. 525–537, 2022.
ista: Koudjinan E, Kaloshin V. 2022. On some invariants of Birkhoff billiards under
conjugacy. Regular and Chaotic Dynamics. 27(6), 525–537.
mla: Koudjinan, Edmond, and Vadim Kaloshin. “On Some Invariants of Birkhoff Billiards
under Conjugacy.” Regular and Chaotic Dynamics, vol. 27, no. 6, Springer
Nature, 2022, pp. 525–37, doi:10.1134/S1560354722050021.
short: E. Koudjinan, V. Kaloshin, Regular and Chaotic Dynamics 27 (2022) 525–537.
date_created: 2023-01-12T12:06:49Z
date_published: 2022-10-03T00:00:00Z
date_updated: 2023-08-04T08:59:14Z
day: '03'
department:
- _id: VaKa
doi: 10.1134/S1560354722050021
ec_funded: 1
external_id:
arxiv:
- '2105.14640'
isi:
- '000865267300002'
intvolume: ' 27'
isi: 1
issue: '6'
keyword:
- Mechanical Engineering
- Applied Mathematics
- Mathematical Physics
- Modeling and Simulation
- Statistical and Nonlinear Physics
- Mathematics (miscellaneous)
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2105.14640
month: '10'
oa: 1
oa_version: Preprint
page: 525-537
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Regular and Chaotic Dynamics
publication_identifier:
eissn:
- 1468-4845
issn:
- 1560-3547
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- relation: erratum
url: https://doi.org/10.1134/s1560354722060107
scopus_import: '1'
status: public
title: On some invariants of Birkhoff billiards under conjugacy
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 27
year: '2022'
...
---
_id: '9435'
abstract:
- lang: eng
text: For any given positive integer l, we prove that every plane deformation of
a circlewhich preserves the 1/2and 1/ (2l + 1) -rational caustics is trivial i.e.
the deformationconsists only of similarities (rescalings and isometries).
article_processing_charge: No
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Edmond
full_name: Koudjinan, Edmond
id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E
last_name: Koudjinan
orcid: 0000-0003-2640-4049
citation:
ama: Kaloshin V, Koudjinan E. Non co-preservation of the 1/2 and 1/(2l+1)-rational
caustics along deformations of circles. 2021.
apa: Kaloshin, V., & Koudjinan, E. (2021). Non co-preservation of the 1/2 and
1/(2l+1)-rational caustics along deformations of circles.
chicago: Kaloshin, Vadim, and Edmond Koudjinan. “Non Co-Preservation of the 1/2
and 1/(2l+1)-Rational Caustics along Deformations of Circles,” 2021.
ieee: V. Kaloshin and E. Koudjinan, “Non co-preservation of the 1/2 and 1/(2l+1)-rational
caustics along deformations of circles.” 2021.
ista: Kaloshin V, Koudjinan E. 2021. Non co-preservation of the 1/2 and 1/(2l+1)-rational
caustics along deformations of circles.
mla: Kaloshin, Vadim, and Edmond Koudjinan. Non Co-Preservation of the 1/2 and
1/(2l+1)-Rational Caustics along Deformations of Circles. 2021.
short: V. Kaloshin, E. Koudjinan, (2021).
date_created: 2021-05-30T13:58:13Z
date_published: 2021-01-01T00:00:00Z
date_updated: 2021-06-01T09:10:22Z
ddc:
- '500'
department:
- _id: VaKa
file:
- access_level: open_access
checksum: b281b5c2e3e90de0646c3eafcb2c6c25
content_type: application/pdf
creator: ekoudjin
date_created: 2021-05-30T13:57:37Z
date_updated: 2021-05-30T13:57:37Z
file_id: '9436'
file_name: CoExistence 2&3 caustics 3_17_6_2_3.pdf
file_size: 353431
relation: main_file
file_date_updated: 2021-05-30T13:57:37Z
has_accepted_license: '1'
language:
- iso: eng
oa: 1
oa_version: Submitted Version
status: public
title: Non co-preservation of the 1/2 and 1/(2l+1)-rational caustics along deformations
of circles
type: preprint
user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87
year: '2021'
...
---
_id: '8414'
abstract:
- lang: eng
text: "Arnold diffusion, which concerns the appearance of chaos in classical mechanics,
is one of the most important problems in the fields of dynamical systems and mathematical
physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted
the efforts of some of the most prominent researchers in mathematics. The question
is whether a typical perturbation of a particular system will result in chaotic
or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and
Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that
that there is topological instability for typical perturbations of five-dimensional
integrable systems (two and a half degrees of freedom).\r\nThis proof realizes
a plan John Mather announced in 2003 but was unable to complete before his death.
Kaloshin and Zhang follow Mather’s strategy but emphasize a more Hamiltonian approach,
tying together normal forms theory, hyperbolic theory, Mather theory, and weak
KAM theory. Offering a complete, clean, and modern explanation of the steps involved
in the proof, and a clear account of background material, this book is designed
to be accessible to students as well as researchers. The result is a critical
contribution to mathematical physics and dynamical systems, especially Hamiltonian
systems."
alternative_title:
- Annals of Mathematics Studies
article_processing_charge: No
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Ke
full_name: Zhang, Ke
last_name: Zhang
citation:
ama: Kaloshin V, Zhang K. Arnold Diffusion for Smooth Systems of Two and a Half
Degrees of Freedom. Vol 208. 1st ed. Princeton University Press; 2020. doi:10.1515/9780691204932
apa: Kaloshin, V., & Zhang, K. (2020). Arnold Diffusion for Smooth Systems
of Two and a Half Degrees of Freedom (1st ed., Vol. 208). Princeton University
Press. https://doi.org/10.1515/9780691204932
chicago: Kaloshin, Vadim, and Ke Zhang. Arnold Diffusion for Smooth Systems of
Two and a Half Degrees of Freedom. 1st ed. Vol. 208. AMS. Princeton University
Press, 2020. https://doi.org/10.1515/9780691204932.
ieee: V. Kaloshin and K. Zhang, Arnold Diffusion for Smooth Systems of Two and
a Half Degrees of Freedom, 1st ed., vol. 208. Princeton University Press,
2020.
ista: Kaloshin V, Zhang K. 2020. Arnold Diffusion for Smooth Systems of Two and
a Half Degrees of Freedom 1st ed., Princeton University Press, 224p.
mla: Kaloshin, Vadim, and Ke Zhang. Arnold Diffusion for Smooth Systems of Two
and a Half Degrees of Freedom. 1st ed., vol. 208, Princeton University Press,
2020, doi:10.1515/9780691204932.
short: V. Kaloshin, K. Zhang, Arnold Diffusion for Smooth Systems of Two and a Half
Degrees of Freedom, 1st ed., Princeton University Press, 2020.
date_created: 2020-09-17T10:41:05Z
date_published: 2020-03-01T00:00:00Z
date_updated: 2021-12-21T10:50:49Z
day: '01'
doi: 10.1515/9780691204932
edition: '1'
extern: '1'
intvolume: ' 208'
language:
- iso: eng
month: '03'
oa_version: None
page: '224'
publication_identifier:
isbn:
- 9-780-6912-0253-2
publication_status: published
publisher: Princeton University Press
quality_controlled: '1'
scopus_import: '1'
series_title: AMS
status: public
title: Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom
type: book
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
volume: 208
year: '2020'
...
---
_id: '8415'
abstract:
- lang: eng
text: 'We consider billiards obtained by removing three strictly convex obstacles
satisfying the non-eclipse condition on the plane. The restriction of the dynamics
to the set of non-escaping orbits is conjugated to a subshift on three symbols
that provides a natural labeling of all periodic orbits. We study the following
inverse problem: does the Marked Length Spectrum (i.e., the set of lengths of
periodic orbits together with their labeling), determine the geometry of the billiard
table? We show that from the Marked Length Spectrum it is possible to recover
the curvature at periodic points of period two, as well as the Lyapunov exponent
of each periodic orbit.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Péter
full_name: Bálint, Péter
last_name: Bálint
- first_name: Jacopo
full_name: De Simoi, Jacopo
last_name: De Simoi
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Martin
full_name: Leguil, Martin
last_name: Leguil
citation:
ama: Bálint P, De Simoi J, Kaloshin V, Leguil M. Marked length spectrum, homoclinic
orbits and the geometry of open dispersing billiards. Communications in Mathematical
Physics. 2019;374(3):1531-1575. doi:10.1007/s00220-019-03448-x
apa: Bálint, P., De Simoi, J., Kaloshin, V., & Leguil, M. (2019). Marked length
spectrum, homoclinic orbits and the geometry of open dispersing billiards. Communications
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-019-03448-x
chicago: Bálint, Péter, Jacopo De Simoi, Vadim Kaloshin, and Martin Leguil. “Marked
Length Spectrum, Homoclinic Orbits and the Geometry of Open Dispersing Billiards.”
Communications in Mathematical Physics. Springer Nature, 2019. https://doi.org/10.1007/s00220-019-03448-x.
ieee: P. Bálint, J. De Simoi, V. Kaloshin, and M. Leguil, “Marked length spectrum,
homoclinic orbits and the geometry of open dispersing billiards,” Communications
in Mathematical Physics, vol. 374, no. 3. Springer Nature, pp. 1531–1575,
2019.
ista: Bálint P, De Simoi J, Kaloshin V, Leguil M. 2019. Marked length spectrum,
homoclinic orbits and the geometry of open dispersing billiards. Communications
in Mathematical Physics. 374(3), 1531–1575.
mla: Bálint, Péter, et al. “Marked Length Spectrum, Homoclinic Orbits and the Geometry
of Open Dispersing Billiards.” Communications in Mathematical Physics,
vol. 374, no. 3, Springer Nature, 2019, pp. 1531–75, doi:10.1007/s00220-019-03448-x.
short: P. Bálint, J. De Simoi, V. Kaloshin, M. Leguil, Communications in Mathematical
Physics 374 (2019) 1531–1575.
date_created: 2020-09-17T10:41:27Z
date_published: 2019-05-09T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '09'
doi: 10.1007/s00220-019-03448-x
extern: '1'
external_id:
arxiv:
- '1809.08947'
intvolume: ' 374'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1809.08947
month: '05'
oa: 1
oa_version: Preprint
page: 1531-1575
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Marked length spectrum, homoclinic orbits and the geometry of open dispersing
billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 374
year: '2019'
...
---
_id: '8416'
abstract:
- lang: eng
text: In this paper, we show that any smooth one-parameter deformations of a strictly
convex integrable billiard table Ω0 preserving the integrability near the boundary
have to be tangent to a finite dimensional space passing through Ω0.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guan
full_name: Huang, Guan
last_name: Huang
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Huang G, Kaloshin V. On the finite dimensionality of integrable deformations
of strictly convex integrable billiard tables. Moscow Mathematical Journal.
2019;19(2):307-327. doi:10.17323/1609-4514-2019-19-2-307-327
apa: Huang, G., & Kaloshin, V. (2019). On the finite dimensionality of integrable
deformations of strictly convex integrable billiard tables. Moscow Mathematical
Journal. American Mathematical Society. https://doi.org/10.17323/1609-4514-2019-19-2-307-327
chicago: Huang, Guan, and Vadim Kaloshin. “On the Finite Dimensionality of Integrable
Deformations of Strictly Convex Integrable Billiard Tables.” Moscow Mathematical
Journal. American Mathematical Society, 2019. https://doi.org/10.17323/1609-4514-2019-19-2-307-327.
ieee: G. Huang and V. Kaloshin, “On the finite dimensionality of integrable deformations
of strictly convex integrable billiard tables,” Moscow Mathematical Journal,
vol. 19, no. 2. American Mathematical Society, pp. 307–327, 2019.
ista: Huang G, Kaloshin V. 2019. On the finite dimensionality of integrable deformations
of strictly convex integrable billiard tables. Moscow Mathematical Journal. 19(2),
307–327.
mla: Huang, Guan, and Vadim Kaloshin. “On the Finite Dimensionality of Integrable
Deformations of Strictly Convex Integrable Billiard Tables.” Moscow Mathematical
Journal, vol. 19, no. 2, American Mathematical Society, 2019, pp. 307–27,
doi:10.17323/1609-4514-2019-19-2-307-327.
short: G. Huang, V. Kaloshin, Moscow Mathematical Journal 19 (2019) 307–327.
date_created: 2020-09-17T10:41:36Z
date_published: 2019-04-01T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '01'
doi: 10.17323/1609-4514-2019-19-2-307-327
extern: '1'
external_id:
arxiv:
- '1809.09341'
intvolume: ' 19'
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1809.09341
month: '04'
oa: 1
oa_version: Preprint
page: 307-327
publication: Moscow Mathematical Journal
publication_identifier:
issn:
- 1609-4514
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: On the finite dimensionality of integrable deformations of strictly convex
integrable billiard tables
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 19
year: '2019'
...
---
_id: '8418'
abstract:
- lang: eng
text: For the Restricted Circular Planar 3 Body Problem, we show that there exists
an open set U in phase space of fixed measure, where the set of initial points
which lead to collision is O(μ120) dense as μ→0.
article_processing_charge: No
article_type: original
author:
- first_name: Marcel
full_name: Guardia, Marcel
last_name: Guardia
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Jianlu
full_name: Zhang, Jianlu
last_name: Zhang
citation:
ama: Guardia M, Kaloshin V, Zhang J. Asymptotic density of collision orbits in the
Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics and
Analysis. 2019;233(2):799-836. doi:10.1007/s00205-019-01368-7
apa: Guardia, M., Kaloshin, V., & Zhang, J. (2019). Asymptotic density of collision
orbits in the Restricted Circular Planar 3 Body Problem. Archive for Rational
Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-019-01368-7
chicago: Guardia, Marcel, Vadim Kaloshin, and Jianlu Zhang. “Asymptotic Density
of Collision Orbits in the Restricted Circular Planar 3 Body Problem.” Archive
for Rational Mechanics and Analysis. Springer Nature, 2019. https://doi.org/10.1007/s00205-019-01368-7.
ieee: M. Guardia, V. Kaloshin, and J. Zhang, “Asymptotic density of collision orbits
in the Restricted Circular Planar 3 Body Problem,” Archive for Rational Mechanics
and Analysis, vol. 233, no. 2. Springer Nature, pp. 799–836, 2019.
ista: Guardia M, Kaloshin V, Zhang J. 2019. Asymptotic density of collision orbits
in the Restricted Circular Planar 3 Body Problem. Archive for Rational Mechanics
and Analysis. 233(2), 799–836.
mla: Guardia, Marcel, et al. “Asymptotic Density of Collision Orbits in the Restricted
Circular Planar 3 Body Problem.” Archive for Rational Mechanics and Analysis,
vol. 233, no. 2, Springer Nature, 2019, pp. 799–836, doi:10.1007/s00205-019-01368-7.
short: M. Guardia, V. Kaloshin, J. Zhang, Archive for Rational Mechanics and Analysis
233 (2019) 799–836.
date_created: 2020-09-17T10:41:51Z
date_published: 2019-03-12T00:00:00Z
date_updated: 2021-01-12T08:19:09Z
day: '12'
doi: 10.1007/s00205-019-01368-7
extern: '1'
intvolume: ' 233'
issue: '2'
keyword:
- Mechanical Engineering
- Mathematics (miscellaneous)
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00205-019-01368-7
month: '03'
oa: 1
oa_version: Published Version
page: 799-836
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
issn:
- 0003-9527
- 1432-0673
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Asymptotic density of collision orbits in the Restricted Circular Planar 3
Body Problem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 233
year: '2019'
...
---
_id: '8417'
abstract:
- lang: eng
text: The restricted planar elliptic three body problem (RPETBP) describes the motion
of a massless particle (a comet or an asteroid) under the gravitational field
of two massive bodies (the primaries, say the Sun and Jupiter) revolving around
their center of mass on elliptic orbits with some positive eccentricity. The aim
of this paper is to show the existence of orbits whose angular momentum performs
arbitrary excursions in a large region. In particular, there exist diffusive orbits,
that is, with a large variation of angular momentum. The leading idea of the proof
consists in analyzing parabolic motions of the comet. By a well-known result of
McGehee, the union of future (resp. past) parabolic orbits is an analytic manifold
P+ (resp. P−). In a properly chosen coordinate system these manifolds are stable
(resp. unstable) manifolds of a manifold at infinity P∞, which we call the manifold
at parabolic infinity. On P∞ it is possible to define two scattering maps, which
contain the map structure of the homoclinic trajectories to it, i.e. orbits parabolic
both in the future and the past. Since the inner dynamics inside P∞ is trivial,
two different scattering maps are used. The combination of these two scattering
maps permits the design of the desired diffusive pseudo-orbits. Using shadowing
techniques and these pseudo orbits we show the existence of true trajectories
of the RPETBP whose angular momentum varies in any predetermined fashion.
article_processing_charge: No
article_type: original
author:
- first_name: Amadeu
full_name: Delshams, Amadeu
last_name: Delshams
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Abraham
full_name: de la Rosa, Abraham
last_name: de la Rosa
- first_name: Tere M.
full_name: Seara, Tere M.
last_name: Seara
citation:
ama: Delshams A, Kaloshin V, de la Rosa A, Seara TM. Global instability in the restricted
planar elliptic three body problem. Communications in Mathematical Physics.
2018;366(3):1173-1228. doi:10.1007/s00220-018-3248-z
apa: Delshams, A., Kaloshin, V., de la Rosa, A., & Seara, T. M. (2018). Global
instability in the restricted planar elliptic three body problem. Communications
in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-018-3248-z
chicago: Delshams, Amadeu, Vadim Kaloshin, Abraham de la Rosa, and Tere M. Seara.
“Global Instability in the Restricted Planar Elliptic Three Body Problem.” Communications
in Mathematical Physics. Springer Nature, 2018. https://doi.org/10.1007/s00220-018-3248-z.
ieee: A. Delshams, V. Kaloshin, A. de la Rosa, and T. M. Seara, “Global instability
in the restricted planar elliptic three body problem,” Communications in Mathematical
Physics, vol. 366, no. 3. Springer Nature, pp. 1173–1228, 2018.
ista: Delshams A, Kaloshin V, de la Rosa A, Seara TM. 2018. Global instability in
the restricted planar elliptic three body problem. Communications in Mathematical
Physics. 366(3), 1173–1228.
mla: Delshams, Amadeu, et al. “Global Instability in the Restricted Planar Elliptic
Three Body Problem.” Communications in Mathematical Physics, vol. 366,
no. 3, Springer Nature, 2018, pp. 1173–228, doi:10.1007/s00220-018-3248-z.
short: A. Delshams, V. Kaloshin, A. de la Rosa, T.M. Seara, Communications in Mathematical
Physics 366 (2018) 1173–1228.
date_created: 2020-09-17T10:41:43Z
date_published: 2018-09-05T00:00:00Z
date_updated: 2021-01-12T08:19:08Z
day: '05'
doi: 10.1007/s00220-018-3248-z
extern: '1'
intvolume: ' 366'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '09'
oa_version: None
page: 1173-1228
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Global instability in the restricted planar elliptic three body problem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 366
year: '2018'
...
---
_id: '8419'
abstract:
- lang: eng
text: "In this survey, we provide a concise introduction to convex billiards and
describe some recent results, obtained by the authors and collaborators, on the
classification of integrable billiards, namely the so-called Birkhoff conjecture.\r\n\r\nThis
article is part of the theme issue ‘Finite dimensional integrable systems: new
trends and methods’."
article_number: '20170419'
article_processing_charge: No
article_type: original
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Alfonso
full_name: Sorrentino, Alfonso
last_name: Sorrentino
citation:
ama: 'Kaloshin V, Sorrentino A. On the integrability of Birkhoff billiards. Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
2018;376(2131). doi:10.1098/rsta.2017.0419'
apa: 'Kaloshin, V., & Sorrentino, A. (2018). On the integrability of Birkhoff
billiards. Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences. The Royal Society. https://doi.org/10.1098/rsta.2017.0419'
chicago: 'Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff
Billiards.” Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences. The Royal Society, 2018. https://doi.org/10.1098/rsta.2017.0419.'
ieee: 'V. Kaloshin and A. Sorrentino, “On the integrability of Birkhoff billiards,”
Philosophical Transactions of the Royal Society A: Mathematical, Physical and
Engineering Sciences, vol. 376, no. 2131. The Royal Society, 2018.'
ista: 'Kaloshin V, Sorrentino A. 2018. On the integrability of Birkhoff billiards.
Philosophical Transactions of the Royal Society A: Mathematical, Physical and
Engineering Sciences. 376(2131), 20170419.'
mla: 'Kaloshin, Vadim, and Alfonso Sorrentino. “On the Integrability of Birkhoff
Billiards.” Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences, vol. 376, no. 2131, 20170419, The Royal
Society, 2018, doi:10.1098/rsta.2017.0419.'
short: 'V. Kaloshin, A. Sorrentino, Philosophical Transactions of the Royal Society
A: Mathematical, Physical and Engineering Sciences 376 (2018).'
date_created: 2020-09-17T10:42:01Z
date_published: 2018-10-28T00:00:00Z
date_updated: 2021-01-12T08:19:09Z
day: '28'
doi: 10.1098/rsta.2017.0419
extern: '1'
intvolume: ' 376'
issue: '2131'
keyword:
- General Engineering
- General Physics and Astronomy
- General Mathematics
language:
- iso: eng
month: '10'
oa_version: None
publication: 'Philosophical Transactions of the Royal Society A: Mathematical, Physical
and Engineering Sciences'
publication_identifier:
issn:
- 1364-503X
- 1471-2962
publication_status: published
publisher: The Royal Society
quality_controlled: '1'
status: public
title: On the integrability of Birkhoff billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 376
year: '2018'
...
---
_id: '8420'
abstract:
- lang: eng
text: We show that in the space of all convex billiard boundaries, the set of boundaries
with rational caustics is dense. More precisely, the set of billiard boundaries
with caustics of rotation number 1/q is polynomially sense in the smooth case,
and exponentially dense in the analytic case.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Ke
full_name: Zhang, Ke
last_name: Zhang
citation:
ama: Kaloshin V, Zhang K. Density of convex billiards with rational caustics. Nonlinearity.
2018;31(11):5214-5234. doi:10.1088/1361-6544/aadc12
apa: Kaloshin, V., & Zhang, K. (2018). Density of convex billiards with rational
caustics. Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/aadc12
chicago: Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational
Caustics.” Nonlinearity. IOP Publishing, 2018. https://doi.org/10.1088/1361-6544/aadc12.
ieee: V. Kaloshin and K. Zhang, “Density of convex billiards with rational caustics,”
Nonlinearity, vol. 31, no. 11. IOP Publishing, pp. 5214–5234, 2018.
ista: Kaloshin V, Zhang K. 2018. Density of convex billiards with rational caustics.
Nonlinearity. 31(11), 5214–5234.
mla: Kaloshin, Vadim, and Ke Zhang. “Density of Convex Billiards with Rational Caustics.”
Nonlinearity, vol. 31, no. 11, IOP Publishing, 2018, pp. 5214–34, doi:10.1088/1361-6544/aadc12.
short: V. Kaloshin, K. Zhang, Nonlinearity 31 (2018) 5214–5234.
date_created: 2020-09-17T10:42:09Z
date_published: 2018-10-15T00:00:00Z
date_updated: 2021-01-12T08:19:10Z
day: '15'
doi: 10.1088/1361-6544/aadc12
extern: '1'
external_id:
arxiv:
- '1706.07968'
intvolume: ' 31'
issue: '11'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1706.07968
month: '10'
oa: 1
oa_version: Preprint
page: 5214-5234
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: Density of convex billiards with rational caustics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 31
year: '2018'
...
---
_id: '8421'
abstract:
- lang: eng
text: 'The classical Birkhoff conjecture claims that the boundary of a strictly
convex integrable billiard table is necessarily an ellipse (or a circle as a special
case). In this article we prove a complete local version of this conjecture: a
small integrable perturbation of an ellipse must be an ellipse. This extends and
completes the result in Avila-De Simoi-Kaloshin, where nearly circular domains
were considered. One of the crucial ideas in the proof is to extend action-angle
coordinates for elliptic billiards into complex domains (with respect to the angle),
and to thoroughly analyze the nature of their complex singularities. As an application,
we are able to prove some spectral rigidity results for elliptic domains.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Alfonso
full_name: Sorrentino, Alfonso
last_name: Sorrentino
citation:
ama: Kaloshin V, Sorrentino A. On the local Birkhoff conjecture for convex billiards.
Annals of Mathematics. 2018;188(1):315-380. doi:10.4007/annals.2018.188.1.6
apa: Kaloshin, V., & Sorrentino, A. (2018). On the local Birkhoff conjecture
for convex billiards. Annals of Mathematics. Annals of Mathematics, Princeton
U. https://doi.org/10.4007/annals.2018.188.1.6
chicago: Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture
for Convex Billiards.” Annals of Mathematics. Annals of Mathematics, Princeton
U, 2018. https://doi.org/10.4007/annals.2018.188.1.6.
ieee: V. Kaloshin and A. Sorrentino, “On the local Birkhoff conjecture for convex
billiards,” Annals of Mathematics, vol. 188, no. 1. Annals of Mathematics,
Princeton U, pp. 315–380, 2018.
ista: Kaloshin V, Sorrentino A. 2018. On the local Birkhoff conjecture for convex
billiards. Annals of Mathematics. 188(1), 315–380.
mla: Kaloshin, Vadim, and Alfonso Sorrentino. “On the Local Birkhoff Conjecture
for Convex Billiards.” Annals of Mathematics, vol. 188, no. 1, Annals of
Mathematics, Princeton U, 2018, pp. 315–80, doi:10.4007/annals.2018.188.1.6.
short: V. Kaloshin, A. Sorrentino, Annals of Mathematics 188 (2018) 315–380.
date_created: 2020-09-17T10:42:22Z
date_published: 2018-07-01T00:00:00Z
date_updated: 2021-01-12T08:19:10Z
day: '01'
doi: 10.4007/annals.2018.188.1.6
extern: '1'
external_id:
arxiv:
- '1612.09194'
intvolume: ' 188'
issue: '1'
keyword:
- Statistics
- Probability and Uncertainty
- Statistics and Probability
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1612.09194
month: '07'
oa: 1
oa_version: Preprint
page: 315-380
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Annals of Mathematics, Princeton U
quality_controlled: '1'
status: public
title: On the local Birkhoff conjecture for convex billiards
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 188
year: '2018'
...
---
_id: '8422'
abstract:
- lang: eng
text: 'The Birkhoff conjecture says that the boundary of a strictly convex integrable
billiard table is necessarily an ellipse. In this article, we consider a stronger
notion of integrability, namely integrability close to the boundary, and prove
a local version of this conjecture: a small perturbation of an ellipse of small
eccentricity which preserves integrability near the boundary, is itself an ellipse.
This extends the result in Avila et al. (Ann Math 184:527–558, ADK16), where integrability
was assumed on a larger set. In particular, it shows that (local) integrability
near the boundary implies global integrability. One of the crucial ideas in the
proof consists in analyzing Taylor expansion of the corresponding action-angle
coordinates with respect to the eccentricity parameter, deriving and studying
higher order conditions for the preservation of integrable rational caustics.'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guan
full_name: Huang, Guan
last_name: Huang
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Alfonso
full_name: Sorrentino, Alfonso
last_name: Sorrentino
citation:
ama: Huang G, Kaloshin V, Sorrentino A. Nearly circular domains which are integrable
close to the boundary are ellipses. Geometric and Functional Analysis.
2018;28(2):334-392. doi:10.1007/s00039-018-0440-4
apa: Huang, G., Kaloshin, V., & Sorrentino, A. (2018). Nearly circular domains
which are integrable close to the boundary are ellipses. Geometric and Functional
Analysis. Springer Nature. https://doi.org/10.1007/s00039-018-0440-4
chicago: Huang, Guan, Vadim Kaloshin, and Alfonso Sorrentino. “Nearly Circular Domains
Which Are Integrable Close to the Boundary Are Ellipses.” Geometric and Functional
Analysis. Springer Nature, 2018. https://doi.org/10.1007/s00039-018-0440-4.
ieee: G. Huang, V. Kaloshin, and A. Sorrentino, “Nearly circular domains which are
integrable close to the boundary are ellipses,” Geometric and Functional Analysis,
vol. 28, no. 2. Springer Nature, pp. 334–392, 2018.
ista: Huang G, Kaloshin V, Sorrentino A. 2018. Nearly circular domains which are
integrable close to the boundary are ellipses. Geometric and Functional Analysis.
28(2), 334–392.
mla: Huang, Guan, et al. “Nearly Circular Domains Which Are Integrable Close to
the Boundary Are Ellipses.” Geometric and Functional Analysis, vol. 28,
no. 2, Springer Nature, 2018, pp. 334–92, doi:10.1007/s00039-018-0440-4.
short: G. Huang, V. Kaloshin, A. Sorrentino, Geometric and Functional Analysis 28
(2018) 334–392.
date_created: 2020-09-17T10:42:30Z
date_published: 2018-03-18T00:00:00Z
date_updated: 2021-01-12T08:19:11Z
day: '18'
doi: 10.1007/s00039-018-0440-4
extern: '1'
external_id:
arxiv:
- '1705.10601'
intvolume: ' 28'
issue: '2'
keyword:
- Geometry and Topology
- Analysis
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1705.10601
month: '03'
oa: 1
oa_version: Preprint
page: 334-392
publication: Geometric and Functional Analysis
publication_identifier:
issn:
- 1016-443X
- 1420-8970
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Nearly circular domains which are integrable close to the boundary are ellipses
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2018'
...
---
_id: '8426'
abstract:
- lang: eng
text: For any strictly convex planar domain Ω ⊂ R2 with a C∞ boundary one can associate
an infinite sequence of spectral invariants introduced by Marvizi–Merlose [5].
These invariants can generically be determined using the spectrum of the Dirichlet
problem of the Laplace operator. A natural question asks if this collection is
sufficient to determine Ω up to isometry. In this paper we give a counterexample,
namely, we present two nonisometric domains Ω and Ω¯ with the same collection
of Marvizi–Melrose invariants. Moreover, each domain has countably many periodic
orbits {Sn}n≥1 (resp. {S¯n}n⩾1) of period going to infinity such that Sn and S¯n
have the same period and perimeter for each n.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Lev
full_name: Buhovsky, Lev
last_name: Buhovsky
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Buhovsky L, Kaloshin V. Nonisometric domains with the same Marvizi-Melrose
invariants. Regular and Chaotic Dynamics. 2018;23:54-59. doi:10.1134/s1560354718010057
apa: Buhovsky, L., & Kaloshin, V. (2018). Nonisometric domains with the same
Marvizi-Melrose invariants. Regular and Chaotic Dynamics. Springer Nature.
https://doi.org/10.1134/s1560354718010057
chicago: Buhovsky, Lev, and Vadim Kaloshin. “Nonisometric Domains with the Same
Marvizi-Melrose Invariants.” Regular and Chaotic Dynamics. Springer Nature,
2018. https://doi.org/10.1134/s1560354718010057.
ieee: L. Buhovsky and V. Kaloshin, “Nonisometric domains with the same Marvizi-Melrose
invariants,” Regular and Chaotic Dynamics, vol. 23. Springer Nature, pp.
54–59, 2018.
ista: Buhovsky L, Kaloshin V. 2018. Nonisometric domains with the same Marvizi-Melrose
invariants. Regular and Chaotic Dynamics. 23, 54–59.
mla: Buhovsky, Lev, and Vadim Kaloshin. “Nonisometric Domains with the Same Marvizi-Melrose
Invariants.” Regular and Chaotic Dynamics, vol. 23, Springer Nature, 2018,
pp. 54–59, doi:10.1134/s1560354718010057.
short: L. Buhovsky, V. Kaloshin, Regular and Chaotic Dynamics 23 (2018) 54–59.
date_created: 2020-09-17T10:43:21Z
date_published: 2018-02-05T00:00:00Z
date_updated: 2021-01-12T08:19:11Z
day: '05'
doi: 10.1134/s1560354718010057
extern: '1'
external_id:
arxiv:
- '1801.00952'
intvolume: ' 23'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1801.00952
month: '02'
oa: 1
oa_version: Preprint
page: 54-59
publication: Regular and Chaotic Dynamics
publication_identifier:
issn:
- 1560-3547
- 1468-4845
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Nonisometric domains with the same Marvizi-Melrose invariants
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 23
year: '2018'
...
---
_id: '8423'
abstract:
- lang: eng
text: In this paper we show that for a generic strictly convex domain, one can recover
the eigendata corresponding to Aubry–Mather periodic orbits of the induced billiard
map from the (maximal) marked length spectrum of the domain.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Guan
full_name: Huang, Guan
last_name: Huang
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Alfonso
full_name: Sorrentino, Alfonso
last_name: Sorrentino
citation:
ama: Huang G, Kaloshin V, Sorrentino A. On the marked length spectrum of generic
strictly convex billiard tables. Duke Mathematical Journal. 2017;167(1):175-209.
doi:10.1215/00127094-2017-0038
apa: Huang, G., Kaloshin, V., & Sorrentino, A. (2017). On the marked length
spectrum of generic strictly convex billiard tables. Duke Mathematical Journal.
Duke University Press. https://doi.org/10.1215/00127094-2017-0038
chicago: Huang, Guan, Vadim Kaloshin, and Alfonso Sorrentino. “On the Marked Length
Spectrum of Generic Strictly Convex Billiard Tables.” Duke Mathematical Journal.
Duke University Press, 2017. https://doi.org/10.1215/00127094-2017-0038.
ieee: G. Huang, V. Kaloshin, and A. Sorrentino, “On the marked length spectrum of
generic strictly convex billiard tables,” Duke Mathematical Journal, vol.
167, no. 1. Duke University Press, pp. 175–209, 2017.
ista: Huang G, Kaloshin V, Sorrentino A. 2017. On the marked length spectrum of
generic strictly convex billiard tables. Duke Mathematical Journal. 167(1), 175–209.
mla: Huang, Guan, et al. “On the Marked Length Spectrum of Generic Strictly Convex
Billiard Tables.” Duke Mathematical Journal, vol. 167, no. 1, Duke University
Press, 2017, pp. 175–209, doi:10.1215/00127094-2017-0038.
short: G. Huang, V. Kaloshin, A. Sorrentino, Duke Mathematical Journal 167 (2017)
175–209.
date_created: 2020-09-17T10:42:42Z
date_published: 2017-12-08T00:00:00Z
date_updated: 2021-01-12T08:19:11Z
day: '08'
doi: 10.1215/00127094-2017-0038
extern: '1'
external_id:
arxiv:
- '1603.08838'
intvolume: ' 167'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1603.08838
month: '12'
oa: 1
oa_version: Preprint
page: 175-209
publication: Duke Mathematical Journal
publication_identifier:
issn:
- 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
status: public
title: On the marked length spectrum of generic strictly convex billiard tables
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 167
year: '2017'
...
---
_id: '8427'
abstract:
- lang: eng
text: We show that any sufficiently (finitely) smooth ℤ₂-symmetric strictly convex
domain sufficiently close to a circle is dynamically spectrally rigid; i.e., all
deformations among domains in the same class that preserve the length of all periodic
orbits of the associated billiard flow must necessarily be isometric deformations.
This gives a partial answer to a question of P. Sarnak.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jacopo
full_name: De Simoi, Jacopo
last_name: De Simoi
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Qiaoling
full_name: Wei, Qiaoling
last_name: Wei
citation:
ama: De Simoi J, Kaloshin V, Wei Q. Dynamical spectral rigidity among Z2-symmetric
strictly convex domains close to a circle. Annals of Mathematics. 2017;186(1):277-314.
doi:10.4007/annals.2017.186.1.7
apa: De Simoi, J., Kaloshin, V., & Wei, Q. (2017). Dynamical spectral rigidity
among Z2-symmetric strictly convex domains close to a circle. Annals of Mathematics.
Annals of Mathematics. https://doi.org/10.4007/annals.2017.186.1.7
chicago: De Simoi, Jacopo, Vadim Kaloshin, and Qiaoling Wei. “Dynamical Spectral
Rigidity among Z2-Symmetric Strictly Convex Domains Close to a Circle.” Annals
of Mathematics. Annals of Mathematics, 2017. https://doi.org/10.4007/annals.2017.186.1.7.
ieee: J. De Simoi, V. Kaloshin, and Q. Wei, “Dynamical spectral rigidity among Z2-symmetric
strictly convex domains close to a circle,” Annals of Mathematics, vol.
186, no. 1. Annals of Mathematics, pp. 277–314, 2017.
ista: De Simoi J, Kaloshin V, Wei Q. 2017. Dynamical spectral rigidity among Z2-symmetric
strictly convex domains close to a circle. Annals of Mathematics. 186(1), 277–314.
mla: De Simoi, Jacopo, et al. “Dynamical Spectral Rigidity among Z2-Symmetric Strictly
Convex Domains Close to a Circle.” Annals of Mathematics, vol. 186, no.
1, Annals of Mathematics, 2017, pp. 277–314, doi:10.4007/annals.2017.186.1.7.
short: J. De Simoi, V. Kaloshin, Q. Wei, Annals of Mathematics 186 (2017) 277–314.
date_created: 2020-09-17T10:46:42Z
date_published: 2017-07-01T00:00:00Z
date_updated: 2021-01-12T08:19:12Z
day: '01'
doi: 10.4007/annals.2017.186.1.7
extern: '1'
external_id:
arxiv:
- '1606.00230'
intvolume: ' 186'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1606.00230
month: '07'
oa: 1
oa_version: Preprint
page: 277-314
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Annals of Mathematics
quality_controlled: '1'
status: public
title: Dynamical spectral rigidity among Z2-symmetric strictly convex domains close
to a circle
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 186
year: '2017'
...
---
_id: '8493'
abstract:
- lang: eng
text: In this paper we study a so-called separatrix map introduced by Zaslavskii–Filonenko
(Sov Phys JETP 27:851–857, 1968) and studied by Treschev (Physica D 116(1–2):21–43,
1998; J Nonlinear Sci 12(1):27–58, 2002), Piftankin (Nonlinearity (19):2617–2644,
2006) Piftankin and Treshchëv (Uspekhi Mat Nauk 62(2(374)):3–108, 2007). We derive
a second order expansion of this map for trigonometric perturbations. In Castejon
et al. (Random iteration of maps of a cylinder and diffusive behavior. Preprint
available at arXiv:1501.03319, 2015), Guardia and Kaloshin (Stochastic diffusive
behavior through big gaps in a priori unstable systems (in preparation), 2015),
and Kaloshin et al. (Normally Hyperbolic Invariant Laminations and diffusive behavior
for the generalized Arnold example away from resonances. Preprint available at
http://www.terpconnect.umd.edu/vkaloshi/, 2015), applying the results of the present
paper, we describe a class of nearly integrable deterministic systems with stochastic
diffusive behavior.
article_processing_charge: No
article_type: original
author:
- first_name: M.
full_name: Guardia, M.
last_name: Guardia
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: J.
full_name: Zhang, J.
last_name: Zhang
citation:
ama: Guardia M, Kaloshin V, Zhang J. A second order expansion of the separatrix
map for trigonometric perturbations of a priori unstable systems. Communications
in Mathematical Physics. 2016;348:321-361. doi:10.1007/s00220-016-2705-9
apa: Guardia, M., Kaloshin, V., & Zhang, J. (2016). A second order expansion
of the separatrix map for trigonometric perturbations of a priori unstable systems.
Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-016-2705-9
chicago: Guardia, M., Vadim Kaloshin, and J. Zhang. “A Second Order Expansion of
the Separatrix Map for Trigonometric Perturbations of a Priori Unstable Systems.”
Communications in Mathematical Physics. Springer Nature, 2016. https://doi.org/10.1007/s00220-016-2705-9.
ieee: M. Guardia, V. Kaloshin, and J. Zhang, “A second order expansion of the separatrix
map for trigonometric perturbations of a priori unstable systems,” Communications
in Mathematical Physics, vol. 348. Springer Nature, pp. 321–361, 2016.
ista: Guardia M, Kaloshin V, Zhang J. 2016. A second order expansion of the separatrix
map for trigonometric perturbations of a priori unstable systems. Communications
in Mathematical Physics. 348, 321–361.
mla: Guardia, M., et al. “A Second Order Expansion of the Separatrix Map for Trigonometric
Perturbations of a Priori Unstable Systems.” Communications in Mathematical
Physics, vol. 348, Springer Nature, 2016, pp. 321–61, doi:10.1007/s00220-016-2705-9.
short: M. Guardia, V. Kaloshin, J. Zhang, Communications in Mathematical Physics
348 (2016) 321–361.
date_created: 2020-09-18T10:45:50Z
date_published: 2016-11-01T00:00:00Z
date_updated: 2021-01-12T08:19:39Z
day: '01'
doi: 10.1007/s00220-016-2705-9
extern: '1'
intvolume: ' 348'
language:
- iso: eng
month: '11'
oa_version: None
page: 321-361
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: A second order expansion of the separatrix map for trigonometric perturbations
of a priori unstable systems
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 348
year: '2016'
...
---
_id: '8494'
abstract:
- lang: eng
text: "We prove a form of Arnold diffusion in the a-priori stable case. Let\r\nH0(p)+ϵH1(θ,p,t),θ∈Tn,p∈Bn,t∈T=R/T,\r\nbe
a nearly integrable system of arbitrary degrees of freedom n⩾2 with a strictly
convex H0. We show that for a “generic” ϵH1, there exists an orbit (θ,p) satisfying\r\n∥p(t)−p(0)∥>l(H1)>0,\r\nwhere
l(H1) is independent of ϵ. The diffusion orbit travels along a codimension-1 resonance,
and the only obstruction to our construction is a finite set of additional resonances.\r\n\r\nFor
the proof we use a combination of geometric and variational methods, and manage
to adapt tools which have recently been developed in the a-priori unstable case."
article_processing_charge: No
article_type: original
author:
- first_name: Patrick
full_name: Bernard, Patrick
last_name: Bernard
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Ke
full_name: Zhang, Ke
last_name: Zhang
citation:
ama: Bernard P, Kaloshin V, Zhang K. Arnold diffusion in arbitrary degrees of freedom
and normally hyperbolic invariant cylinders. Acta Mathematica. 2016;217(1):1-79.
doi:10.1007/s11511-016-0141-5
apa: Bernard, P., Kaloshin, V., & Zhang, K. (2016). Arnold diffusion in arbitrary
degrees of freedom and normally hyperbolic invariant cylinders. Acta Mathematica.
Institut Mittag-Leffler. https://doi.org/10.1007/s11511-016-0141-5
chicago: Bernard, Patrick, Vadim Kaloshin, and Ke Zhang. “Arnold Diffusion in Arbitrary
Degrees of Freedom and Normally Hyperbolic Invariant Cylinders.” Acta Mathematica.
Institut Mittag-Leffler, 2016. https://doi.org/10.1007/s11511-016-0141-5.
ieee: P. Bernard, V. Kaloshin, and K. Zhang, “Arnold diffusion in arbitrary degrees
of freedom and normally hyperbolic invariant cylinders,” Acta Mathematica,
vol. 217, no. 1. Institut Mittag-Leffler, pp. 1–79, 2016.
ista: Bernard P, Kaloshin V, Zhang K. 2016. Arnold diffusion in arbitrary degrees
of freedom and normally hyperbolic invariant cylinders. Acta Mathematica. 217(1),
1–79.
mla: Bernard, Patrick, et al. “Arnold Diffusion in Arbitrary Degrees of Freedom
and Normally Hyperbolic Invariant Cylinders.” Acta Mathematica, vol. 217,
no. 1, Institut Mittag-Leffler, 2016, pp. 1–79, doi:10.1007/s11511-016-0141-5.
short: P. Bernard, V. Kaloshin, K. Zhang, Acta Mathematica 217 (2016) 1–79.
date_created: 2020-09-18T10:46:07Z
date_published: 2016-09-28T00:00:00Z
date_updated: 2021-01-12T08:19:39Z
day: '28'
doi: 10.1007/s11511-016-0141-5
extern: '1'
intvolume: ' 217'
issue: '1'
language:
- iso: eng
month: '09'
oa_version: None
page: 1-79
publication: Acta Mathematica
publication_identifier:
issn:
- 0001-5962
publication_status: published
publisher: Institut Mittag-Leffler
quality_controlled: '1'
status: public
title: Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant
cylinders
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 217
year: '2016'
...
---
_id: '8496'
article_processing_charge: No
article_type: original
author:
- first_name: Artur
full_name: Avila, Artur
last_name: Avila
- first_name: Jacopo
full_name: De Simoi, Jacopo
last_name: De Simoi
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Avila A, De Simoi J, Kaloshin V. An integrable deformation of an ellipse of
small eccentricity is an ellipse. Annals of Mathematics. 2016;184(2):527-558.
doi:10.4007/annals.2016.184.2.5
apa: Avila, A., De Simoi, J., & Kaloshin, V. (2016). An integrable deformation
of an ellipse of small eccentricity is an ellipse. Annals of Mathematics.
Princeton University Press. https://doi.org/10.4007/annals.2016.184.2.5
chicago: Avila, Artur, Jacopo De Simoi, and Vadim Kaloshin. “An Integrable Deformation
of an Ellipse of Small Eccentricity Is an Ellipse.” Annals of Mathematics.
Princeton University Press, 2016. https://doi.org/10.4007/annals.2016.184.2.5.
ieee: A. Avila, J. De Simoi, and V. Kaloshin, “An integrable deformation of an ellipse
of small eccentricity is an ellipse,” Annals of Mathematics, vol. 184,
no. 2. Princeton University Press, pp. 527–558, 2016.
ista: Avila A, De Simoi J, Kaloshin V. 2016. An integrable deformation of an ellipse
of small eccentricity is an ellipse. Annals of Mathematics. 184(2), 527–558.
mla: Avila, Artur, et al. “An Integrable Deformation of an Ellipse of Small Eccentricity
Is an Ellipse.” Annals of Mathematics, vol. 184, no. 2, Princeton University
Press, 2016, pp. 527–58, doi:10.4007/annals.2016.184.2.5.
short: A. Avila, J. De Simoi, V. Kaloshin, Annals of Mathematics 184 (2016) 527–558.
date_created: 2020-09-18T10:46:22Z
date_published: 2016-09-01T00:00:00Z
date_updated: 2021-01-12T08:19:40Z
day: '01'
doi: 10.4007/annals.2016.184.2.5
extern: '1'
intvolume: ' 184'
issue: '2'
language:
- iso: eng
month: '09'
oa_version: None
page: 527-558
publication: Annals of Mathematics
publication_identifier:
issn:
- 0003-486X
publication_status: published
publisher: Princeton University Press
quality_controlled: '1'
status: public
title: An integrable deformation of an ellipse of small eccentricity is an ellipse
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 184
year: '2016'
...
---
_id: '8497'
abstract:
- lang: eng
text: "We study the dynamics of the restricted planar three-body problem near mean
motion resonances, i.e. a resonance involving the Keplerian periods of the two
lighter bodies revolving around the most massive one. This problem is often used
to model Sun–Jupiter–asteroid systems. For the primaries (Sun and Jupiter), we
pick a realistic mass ratio μ=10−3 and a small eccentricity e0>0. The main result
is a construction of a variety of non local diffusing orbits which show a drastic
change of the osculating (instant) eccentricity of the asteroid, while the osculating
semi major axis is kept almost constant. The proof relies on the careful analysis
of the circular problem, which has a hyperbolic structure, but for which diffusion
is prevented by KAM tori. In the proof we verify certain non-degeneracy conditions
numerically.\r\n\r\nBased on the work of Treschev, it is natural to conjecture
that the time of diffusion for this problem is ∼−ln(μe0)μ3/2e0. We expect our
instability mechanism to apply to realistic values of e0 and we give heuristic
arguments in its favor. If so, the applicability of Nekhoroshev theory to the
three-body problem as well as the long time stability become questionable.\r\n\r\nIt
is well known that, in the Asteroid Belt, located between the orbits of Mars and
Jupiter, the distribution of asteroids has the so-called Kirkwood gaps exactly
at mean motion resonances of low order. Our mechanism gives a possible explanation
of their existence. To relate the existence of Kirkwood gaps with Arnol'd diffusion,
we also state a conjecture on its existence for a typical ϵ-perturbation of the
product of the pendulum and the rotator. Namely, we predict that a positive conditional
measure of initial conditions concentrated in the main resonance exhibits Arnol’d
diffusion on time scales −lnϵϵ2."
article_processing_charge: No
article_type: original
author:
- first_name: Jacques
full_name: Féjoz, Jacques
last_name: Féjoz
- first_name: Marcel
full_name: Guàrdia, Marcel
last_name: Guàrdia
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Pablo
full_name: Roldán, Pablo
last_name: Roldán
citation:
ama: Féjoz J, Guàrdia M, Kaloshin V, Roldán P. Kirkwood gaps and diffusion along
mean motion resonances in the restricted planar three-body problem. Journal
of the European Mathematical Society. 2016;18(10):2315-2403. doi:10.4171/jems/642
apa: Féjoz, J., Guàrdia, M., Kaloshin, V., & Roldán, P. (2016). Kirkwood gaps
and diffusion along mean motion resonances in the restricted planar three-body
problem. Journal of the European Mathematical Society. European Mathematical
Society Publishing House. https://doi.org/10.4171/jems/642
chicago: Féjoz, Jacques, Marcel Guàrdia, Vadim Kaloshin, and Pablo Roldán. “Kirkwood
Gaps and Diffusion along Mean Motion Resonances in the Restricted Planar Three-Body
Problem.” Journal of the European Mathematical Society. European Mathematical
Society Publishing House, 2016. https://doi.org/10.4171/jems/642.
ieee: J. Féjoz, M. Guàrdia, V. Kaloshin, and P. Roldán, “Kirkwood gaps and diffusion
along mean motion resonances in the restricted planar three-body problem,” Journal
of the European Mathematical Society, vol. 18, no. 10. European Mathematical
Society Publishing House, pp. 2315–2403, 2016.
ista: Féjoz J, Guàrdia M, Kaloshin V, Roldán P. 2016. Kirkwood gaps and diffusion
along mean motion resonances in the restricted planar three-body problem. Journal
of the European Mathematical Society. 18(10), 2315–2403.
mla: Féjoz, Jacques, et al. “Kirkwood Gaps and Diffusion along Mean Motion Resonances
in the Restricted Planar Three-Body Problem.” Journal of the European Mathematical
Society, vol. 18, no. 10, European Mathematical Society Publishing House,
2016, pp. 2315–403, doi:10.4171/jems/642.
short: J. Féjoz, M. Guàrdia, V. Kaloshin, P. Roldán, Journal of the European Mathematical
Society 18 (2016) 2315–2403.
date_created: 2020-09-18T10:46:31Z
date_published: 2016-09-19T00:00:00Z
date_updated: 2021-01-12T08:19:41Z
day: '19'
doi: 10.4171/jems/642
extern: '1'
intvolume: ' 18'
issue: '10'
language:
- iso: eng
month: '09'
oa_version: None
page: 2315-2403
publication: Journal of the European Mathematical Society
publication_identifier:
issn:
- 1435-9855
publication_status: published
publisher: European Mathematical Society Publishing House
quality_controlled: '1'
status: public
title: Kirkwood gaps and diffusion along mean motion resonances in the restricted
planar three-body problem
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 18
year: '2016'
...