---
_id: '9973'
abstract:
- lang: eng
text: In this article we introduce a complete gradient estimate for symmetric quantum
Markov semigroups on von Neumann algebras equipped with a normal faithful tracial
state, which implies semi-convexity of the entropy with respect to the recently
introduced noncommutative 2-Wasserstein distance. We show that this complete gradient
estimate is stable under tensor products and free products and establish its validity
for a number of examples. As an application we prove a complete modified logarithmic
Sobolev inequality with optimal constant for Poisson-type semigroups on free group
factors.
acknowledgement: Both authors would like to thank Jan Maas for fruitful discussions
and helpful comments.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Melchior
full_name: Wirth, Melchior
id: 88644358-0A0E-11EA-8FA5-49A33DDC885E
last_name: Wirth
orcid: 0000-0002-0519-4241
- first_name: Haonan
full_name: Zhang, Haonan
id: D8F41E38-9E66-11E9-A9E2-65C2E5697425
last_name: Zhang
citation:
ama: Wirth M, Zhang H. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 2021;387:761–791. doi:10.1007/s00220-021-04199-4
apa: Wirth, M., & Zhang, H. (2021). Complete gradient estimates of quantum Markov
semigroups. Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-021-04199-4
chicago: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics. Springer Nature,
2021. https://doi.org/10.1007/s00220-021-04199-4.
ieee: M. Wirth and H. Zhang, “Complete gradient estimates of quantum Markov semigroups,”
Communications in Mathematical Physics, vol. 387. Springer Nature, pp.
761–791, 2021.
ista: Wirth M, Zhang H. 2021. Complete gradient estimates of quantum Markov semigroups.
Communications in Mathematical Physics. 387, 761–791.
mla: Wirth, Melchior, and Haonan Zhang. “Complete Gradient Estimates of Quantum
Markov Semigroups.” Communications in Mathematical Physics, vol. 387, Springer
Nature, 2021, pp. 761–791, doi:10.1007/s00220-021-04199-4.
short: M. Wirth, H. Zhang, Communications in Mathematical Physics 387 (2021) 761–791.
date_created: 2021-08-30T10:07:44Z
date_published: 2021-08-30T00:00:00Z
date_updated: 2023-08-11T11:09:07Z
day: '30'
ddc:
- '621'
department:
- _id: JaMa
doi: 10.1007/s00220-021-04199-4
ec_funded: 1
external_id:
arxiv:
- '2007.13506'
isi:
- '000691214200001'
file:
- access_level: open_access
checksum: 8a602f916b1c2b0dc1159708b7cb204b
content_type: application/pdf
creator: cchlebak
date_created: 2021-09-08T07:34:24Z
date_updated: 2021-09-08T09:46:34Z
file_id: '9990'
file_name: 2021_CommunMathPhys_Wirth.pdf
file_size: 505971
relation: main_file
file_date_updated: 2021-09-08T09:46:34Z
has_accepted_license: '1'
intvolume: ' 387'
isi: 1
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 761–791
project:
- _id: B67AFEDC-15C9-11EA-A837-991A96BB2854
name: IST Austria Open Access Fund
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Communications in Mathematical Physics
publication_identifier:
eissn:
- 1432-0916
issn:
- 0010-3616
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Complete gradient estimates of quantum Markov semigroups
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 387
year: '2021'
...
---
_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: '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: '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: '8498'
abstract:
- lang: eng
text: "In the present note we announce a proof of a strong form of Arnold diffusion
for smooth convex Hamiltonian systems. Let ${\\mathbb T}^2$ be a 2-dimensional
torus and B2 be the unit ball around the origin in ${\\mathbb R}^2$ . Fix ρ >
0. Our main result says that for a 'generic' time-periodic perturbation of an
integrable system of two degrees of freedom $H_0(p)+\\varepsilon H_1(\\theta,p,t),\\quad
\\ \\theta\\in {\\mathbb T}^2,\\ p\\in B^2,\\ t\\in {\\mathbb T}={\\mathbb R}/{\\mathbb
Z}$ , with a strictly convex H0, there exists a ρ-dense orbit (θε, pε, t)(t) in
${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ , namely, a ρ-neighborhood of
the orbit contains ${\\mathbb T}^2 \\times B^2 \\times {\\mathbb T}$ .\r\n\r\nOur
proof is a combination of geometric and variational methods. The fundamental elements
of the construction are the usage of crumpled normally hyperbolic invariant cylinders
from [9], flower and simple normally hyperbolic invariant manifolds from [36]
as well as their kissing property at a strong double resonance. This allows us
to build a 'connected' net of three-dimensional normally hyperbolic invariant
manifolds. To construct diffusing orbits along this net we employ a version of
the Mather variational method [41] equipped with weak KAM theory [28], proposed
by Bernard in [7]."
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: K
full_name: Zhang, K
last_name: Zhang
citation:
ama: Kaloshin V, Zhang K. Arnold diffusion for smooth convex systems of two and
a half degrees of freedom. Nonlinearity. 2015;28(8):2699-2720. doi:10.1088/0951-7715/28/8/2699
apa: Kaloshin, V., & Zhang, K. (2015). Arnold diffusion for smooth convex systems
of two and a half degrees of freedom. Nonlinearity. IOP Publishing. https://doi.org/10.1088/0951-7715/28/8/2699
chicago: Kaloshin, Vadim, and K Zhang. “Arnold Diffusion for Smooth Convex Systems
of Two and a Half Degrees of Freedom.” Nonlinearity. IOP Publishing, 2015.
https://doi.org/10.1088/0951-7715/28/8/2699.
ieee: V. Kaloshin and K. Zhang, “Arnold diffusion for smooth convex systems of two
and a half degrees of freedom,” Nonlinearity, vol. 28, no. 8. IOP Publishing,
pp. 2699–2720, 2015.
ista: Kaloshin V, Zhang K. 2015. Arnold diffusion for smooth convex systems of two
and a half degrees of freedom. Nonlinearity. 28(8), 2699–2720.
mla: Kaloshin, Vadim, and K. Zhang. “Arnold Diffusion for Smooth Convex Systems
of Two and a Half Degrees of Freedom.” Nonlinearity, vol. 28, no. 8, IOP
Publishing, 2015, pp. 2699–720, doi:10.1088/0951-7715/28/8/2699.
short: V. Kaloshin, K. Zhang, Nonlinearity 28 (2015) 2699–2720.
date_created: 2020-09-18T10:46:43Z
date_published: 2015-06-30T00:00:00Z
date_updated: 2021-01-12T08:19:41Z
day: '30'
doi: 10.1088/0951-7715/28/8/2699
extern: '1'
intvolume: ' 28'
issue: '8'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa_version: None
page: 2699-2720
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: Arnold diffusion for smooth convex systems of two and a half degrees of freedom
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 28
year: '2015'
...
---
_id: '8502'
abstract:
- lang: eng
text: 'The famous ergodic hypothesis suggests that for a typical Hamiltonian on
a typical energy surface nearly all trajectories are dense. KAM theory disproves
it. Ehrenfest (The Conceptual Foundations of the Statistical Approach in Mechanics.
Ithaca, NY: Cornell University Press, 1959) and Birkhoff (Collected Math Papers.
Vol 2, New York: Dover, pp 462–465, 1968) stated the quasi-ergodic hypothesis
claiming that a typical Hamiltonian on a typical energy surface has a dense orbit.
This question is wide open. Herman (Proceedings of the International Congress
of Mathematicians, Vol II (Berlin, 1998). Doc Math 1998, Extra Vol II, Berlin:
Int Math Union, pp 797–808, 1998) proposed to look for an example of a Hamiltonian
near H0(I)=⟨I,I⟩2 with a dense orbit on the unit energy surface. In this paper
we construct a Hamiltonian H0(I)+εH1(θ,I,ε) which has an orbit dense in a set
of maximal Hausdorff dimension equal to 5 on the unit energy surface.'
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: Maria
full_name: Saprykina, Maria
last_name: Saprykina
citation:
ama: Kaloshin V, Saprykina M. An example of a nearly integrable Hamiltonian system
with a trajectory dense in a set of maximal Hausdorff dimension. Communications
in Mathematical Physics. 2012;315(3):643-697. doi:10.1007/s00220-012-1532-x
apa: Kaloshin, V., & Saprykina, M. (2012). An example of a nearly integrable
Hamiltonian system with a trajectory dense in a set of maximal Hausdorff dimension.
Communications in Mathematical Physics. Springer Nature. https://doi.org/10.1007/s00220-012-1532-x
chicago: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable
Hamiltonian System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.”
Communications in Mathematical Physics. Springer Nature, 2012. https://doi.org/10.1007/s00220-012-1532-x.
ieee: V. Kaloshin and M. Saprykina, “An example of a nearly integrable Hamiltonian
system with a trajectory dense in a set of maximal Hausdorff dimension,” Communications
in Mathematical Physics, vol. 315, no. 3. Springer Nature, pp. 643–697, 2012.
ista: Kaloshin V, Saprykina M. 2012. An example of a nearly integrable Hamiltonian
system with a trajectory dense in a set of maximal Hausdorff dimension. Communications
in Mathematical Physics. 315(3), 643–697.
mla: Kaloshin, Vadim, and Maria Saprykina. “An Example of a Nearly Integrable Hamiltonian
System with a Trajectory Dense in a Set of Maximal Hausdorff Dimension.” Communications
in Mathematical Physics, vol. 315, no. 3, Springer Nature, 2012, pp. 643–97,
doi:10.1007/s00220-012-1532-x.
short: V. Kaloshin, M. Saprykina, Communications in Mathematical Physics 315 (2012)
643–697.
date_created: 2020-09-18T10:47:16Z
date_published: 2012-11-01T00:00:00Z
date_updated: 2021-01-12T08:19:44Z
day: '01'
doi: 10.1007/s00220-012-1532-x
extern: '1'
intvolume: ' 315'
issue: '3'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '11'
oa_version: None
page: 643-697
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: An example of a nearly integrable Hamiltonian system with a trajectory dense
in a set of maximal Hausdorff dimension
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 315
year: '2012'
...
---
_id: '8525'
abstract:
- lang: eng
text: Let M be a smooth compact manifold of dimension at least 2 and Diffr(M) be
the space of C r smooth diffeomorphisms of M. Associate to each diffeomorphism
f;isin; Diffr(M) the sequence P n (f) of the number of isolated periodic points
for f of period n. In this paper we exhibit an open set N in the space of diffeomorphisms
Diffr(M) such for a Baire generic diffeomorphism f∈N the number of periodic points
P n f grows with a period n faster than any following sequence of numbers {a n
} n ∈ Z + along a subsequence, i.e. P n (f)>a ni for some n i →∞ with i→∞. In
the cases of surface diffeomorphisms, i.e. dim M≡2, an open set N with a supergrowth
of the number of periodic points is a Newhouse domain. A proof of the man result
is based on the Gontchenko–Shilnikov–Turaev Theorem [GST]. A complete proof of
that theorem is also presented.
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
citation:
ama: Kaloshin V. Generic diffeomorphisms with superexponential growth of number
of periodic orbits. Communications in Mathematical Physics. 2000;211:253-271.
doi:10.1007/s002200050811
apa: Kaloshin, V. (2000). Generic diffeomorphisms with superexponential growth of
number of periodic orbits. Communications in Mathematical Physics. Springer
Nature. https://doi.org/10.1007/s002200050811
chicago: Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth
of Number of Periodic Orbits.” Communications in Mathematical Physics.
Springer Nature, 2000. https://doi.org/10.1007/s002200050811.
ieee: V. Kaloshin, “Generic diffeomorphisms with superexponential growth of number
of periodic orbits,” Communications in Mathematical Physics, vol. 211.
Springer Nature, pp. 253–271, 2000.
ista: Kaloshin V. 2000. Generic diffeomorphisms with superexponential growth of
number of periodic orbits. Communications in Mathematical Physics. 211, 253–271.
mla: Kaloshin, Vadim. “Generic Diffeomorphisms with Superexponential Growth of Number
of Periodic Orbits.” Communications in Mathematical Physics, vol. 211,
Springer Nature, 2000, pp. 253–71, doi:10.1007/s002200050811.
short: V. Kaloshin, Communications in Mathematical Physics 211 (2000) 253–271.
date_created: 2020-09-18T10:50:20Z
date_published: 2000-04-01T00:00:00Z
date_updated: 2021-01-12T08:19:52Z
day: '01'
doi: 10.1007/s002200050811
extern: '1'
intvolume: ' 211'
keyword:
- Mathematical Physics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '04'
oa_version: None
page: 253-271
publication: Communications in Mathematical Physics
publication_identifier:
issn:
- 0010-3616
- 1432-0916
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: Generic diffeomorphisms with superexponential growth of number of periodic
orbits
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 211
year: '2000'
...
---
_id: '8527'
abstract:
- lang: eng
text: We introduce a new potential-theoretic definition of the dimension spectrum of
a probability measure for q > 1 and explain its relation to prior definitions.
We apply this definition to prove that if and is a Borel probability measure
with compact support in , then under almost every linear transformation from to
, the q-dimension of the image of is ; in particular, the q-dimension of is
preserved provided . We also present results on the preservation of information
dimension and pointwise dimension. Finally, for and q > 2 we give examples for
which is not preserved by any linear transformation into . All results for typical
linear transformations are also proved for typical (in the sense of prevalence)
continuously differentiable functions.
article_processing_charge: No
article_type: original
author:
- first_name: Brian R
full_name: Hunt, Brian R
last_name: Hunt
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Hunt BR, Kaloshin V. How projections affect the dimension spectrum of fractal
measures. Nonlinearity. 1997;10(5):1031-1046. doi:10.1088/0951-7715/10/5/002
apa: Hunt, B. R., & Kaloshin, V. (1997). How projections affect the dimension
spectrum of fractal measures. Nonlinearity. IOP Publishing. https://doi.org/10.1088/0951-7715/10/5/002
chicago: Hunt, Brian R, and Vadim Kaloshin. “How Projections Affect the Dimension
Spectrum of Fractal Measures.” Nonlinearity. IOP Publishing, 1997. https://doi.org/10.1088/0951-7715/10/5/002.
ieee: B. R. Hunt and V. Kaloshin, “How projections affect the dimension spectrum
of fractal measures,” Nonlinearity, vol. 10, no. 5. IOP Publishing, pp.
1031–1046, 1997.
ista: Hunt BR, Kaloshin V. 1997. How projections affect the dimension spectrum of
fractal measures. Nonlinearity. 10(5), 1031–1046.
mla: Hunt, Brian R., and Vadim Kaloshin. “How Projections Affect the Dimension Spectrum
of Fractal Measures.” Nonlinearity, vol. 10, no. 5, IOP Publishing, 1997,
pp. 1031–46, doi:10.1088/0951-7715/10/5/002.
short: B.R. Hunt, V. Kaloshin, Nonlinearity 10 (1997) 1031–1046.
date_created: 2020-09-18T10:50:41Z
date_published: 1997-06-19T00:00:00Z
date_updated: 2021-01-12T08:19:53Z
day: '19'
doi: 10.1088/0951-7715/10/5/002
extern: '1'
intvolume: ' 10'
issue: '5'
keyword:
- Mathematical Physics
- General Physics and Astronomy
- Applied Mathematics
- Statistical and Nonlinear Physics
language:
- iso: eng
month: '06'
oa_version: None
page: 1031-1046
publication: Nonlinearity
publication_identifier:
issn:
- 0951-7715
- 1361-6544
publication_status: published
publisher: IOP Publishing
quality_controlled: '1'
status: public
title: How projections affect the dimension spectrum of fractal measures
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 10
year: '1997'
...