---
_id: '8501'
abstract:
- lang: eng
text: In this paper, we study small perturbations of a class of non-convex integrable
Hamiltonians with two degrees of freedom, and we prove a result of diffusion for
an open and dense set of perturbations, with an optimal time of diffusion which
grows linearly with respect to the inverse of the size of the perturbation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Abed
full_name: Bounemoura, Abed
last_name: Bounemoura
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Bounemoura A, Kaloshin V. Generic fast diffusion for a class of non-convex
Hamiltonians with two degrees of freedom. Moscow Mathematical Journal.
2014;14(2):181-203. doi:10.17323/1609-4514-2014-14-2-181-203
apa: Bounemoura, A., & Kaloshin, V. (2014). Generic fast diffusion for a class
of non-convex Hamiltonians with two degrees of freedom. Moscow Mathematical
Journal. Independent University of Moscow. https://doi.org/10.17323/1609-4514-2014-14-2-181-203
chicago: Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class
of Non-Convex Hamiltonians with Two Degrees of Freedom.” Moscow Mathematical
Journal. Independent University of Moscow, 2014. https://doi.org/10.17323/1609-4514-2014-14-2-181-203.
ieee: A. Bounemoura and V. Kaloshin, “Generic fast diffusion for a class of non-convex
Hamiltonians with two degrees of freedom,” Moscow Mathematical Journal,
vol. 14, no. 2. Independent University of Moscow, pp. 181–203, 2014.
ista: Bounemoura A, Kaloshin V. 2014. Generic fast diffusion for a class of non-convex
Hamiltonians with two degrees of freedom. Moscow Mathematical Journal. 14(2),
181–203.
mla: Bounemoura, Abed, and Vadim Kaloshin. “Generic Fast Diffusion for a Class of
Non-Convex Hamiltonians with Two Degrees of Freedom.” Moscow Mathematical Journal,
vol. 14, no. 2, Independent University of Moscow, 2014, pp. 181–203, doi:10.17323/1609-4514-2014-14-2-181-203.
short: A. Bounemoura, V. Kaloshin, Moscow Mathematical Journal 14 (2014) 181–203.
date_created: 2020-09-18T10:47:09Z
date_published: 2014-04-01T00:00:00Z
date_updated: 2021-01-12T08:19:43Z
day: '01'
doi: 10.17323/1609-4514-2014-14-2-181-203
extern: '1'
external_id:
arxiv:
- '1304.3050'
intvolume: ' 14'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
month: '04'
oa_version: Preprint
page: 181-203
publication: Moscow Mathematical Journal
publication_identifier:
issn:
- 1609-3321
- 1609-4514
publication_status: published
publisher: Independent University of Moscow
quality_controlled: '1'
status: public
title: Generic fast diffusion for a class of non-convex Hamiltonians with two degrees
of freedom
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 14
year: '2014'
...
---
_id: '9166'
abstract:
- lang: eng
text: Light-activated self-propelled colloids are synthesized and their active motion
is studied using optical microscopy. We propose a versatile route using different
photoactive materials, and demonstrate a multiwavelength activation and propulsion.
Thanks to the photoelectrochemical properties of two semiconductor materials (α-Fe2O3
and TiO2), a light with an energy higher than the bandgap triggers the reaction
of decomposition of hydrogen peroxide and produces a chemical cloud around the
particle. It induces a phoretic attraction with neighbouring colloids as well
as an osmotic self-propulsion of the particle on the substrate. We use these mechanisms
to form colloidal cargos as well as self-propelled particles where the light-activated
component is embedded into a dielectric sphere. The particles are self-propelled
along a direction otherwise randomized by thermal fluctuations, and exhibit a
persistent random walk. For sufficient surface density, the particles spontaneously
form ‘living crystals’ which are mobile, break apart and reform. Steering the
particle with an external magnetic field, we show that the formation of the dense
phase results from the collisions heads-on of the particles. This effect is intrinsically
non-equilibrium and a novel principle of organization for systems without detailed
balance. Engineering families of particles self-propelled by different wavelength
demonstrate a good understanding of both the physics and the chemistry behind
the system and points to a general route for designing new families of self-propelled
particles.
article_number: '20130372'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Jérémie A
full_name: Palacci, Jérémie A
id: 8fb92548-2b22-11eb-b7c1-a3f0d08d7c7d
last_name: Palacci
orcid: 0000-0002-7253-9465
- first_name: S.
full_name: Sacanna, S.
last_name: Sacanna
- first_name: S.-H.
full_name: Kim, S.-H.
last_name: Kim
- first_name: G.-R.
full_name: Yi, G.-R.
last_name: Yi
- first_name: D. J.
full_name: Pine, D. J.
last_name: Pine
- first_name: P. M.
full_name: Chaikin, P. M.
last_name: Chaikin
citation:
ama: 'Palacci JA, Sacanna S, Kim S-H, Yi G-R, Pine DJ, Chaikin PM. Light-activated
self-propelled colloids. Philosophical Transactions of the Royal Society A:
Mathematical, Physical and Engineering Sciences. 2014;372(2029). doi:10.1098/rsta.2013.0372'
apa: 'Palacci, J. A., Sacanna, S., Kim, S.-H., Yi, G.-R., Pine, D. J., & Chaikin,
P. M. (2014). Light-activated self-propelled colloids. Philosophical Transactions
of the Royal Society A: Mathematical, Physical and Engineering Sciences. The
Royal Society. https://doi.org/10.1098/rsta.2013.0372'
chicago: 'Palacci, Jérémie A, S. Sacanna, S.-H. Kim, G.-R. Yi, D. J. Pine, and P.
M. Chaikin. “Light-Activated Self-Propelled Colloids.” Philosophical Transactions
of the Royal Society A: Mathematical, Physical and Engineering Sciences. The
Royal Society, 2014. https://doi.org/10.1098/rsta.2013.0372.'
ieee: 'J. A. Palacci, S. Sacanna, S.-H. Kim, G.-R. Yi, D. J. Pine, and P. M. Chaikin,
“Light-activated self-propelled colloids,” Philosophical Transactions of the
Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 372,
no. 2029. The Royal Society, 2014.'
ista: 'Palacci JA, Sacanna S, Kim S-H, Yi G-R, Pine DJ, Chaikin PM. 2014. Light-activated
self-propelled colloids. Philosophical Transactions of the Royal Society A: Mathematical,
Physical and Engineering Sciences. 372(2029), 20130372.'
mla: 'Palacci, Jérémie A., et al. “Light-Activated Self-Propelled Colloids.” Philosophical
Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences,
vol. 372, no. 2029, 20130372, The Royal Society, 2014, doi:10.1098/rsta.2013.0372.'
short: 'J.A. Palacci, S. Sacanna, S.-H. Kim, G.-R. Yi, D.J. Pine, P.M. Chaikin,
Philosophical Transactions of the Royal Society A: Mathematical, Physical and
Engineering Sciences 372 (2014).'
date_created: 2021-02-18T14:31:11Z
date_published: 2014-11-28T00:00:00Z
date_updated: 2021-02-22T10:44:16Z
day: '28'
doi: 10.1098/rsta.2013.0372
extern: '1'
external_id:
arxiv:
- '1410.7278'
pmid:
- '25332383'
intvolume: ' 372'
issue: '2029'
keyword:
- General Engineering
- General Physics and Astronomy
- General Mathematics
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1098/rsta.2013.0372
month: '11'
oa: 1
oa_version: Published Version
pmid: 1
publication: 'Philosophical Transactions of the Royal Society A: Mathematical, Physical
and Engineering Sciences'
publication_identifier:
eissn:
- 1471-2962
issn:
- 1364-503X
publication_status: published
publisher: The Royal Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: Light-activated self-propelled colloids
type: journal_article
user_id: D865714E-FA4E-11E9-B85B-F5C5E5697425
volume: 372
year: '2014'
...
---
_id: '8504'
abstract:
- lang: eng
text: In this paper we present a surprising example of a Cr unimodal map of an interval
f:I→I whose number of periodic points Pn(f)=∣{x∈I:fnx=x}∣ grows faster than any
ahead given sequence along a subsequence nk=3k. This example also shows that ‘non-flatness’
of critical points is necessary for the Martens–de Melo–van Strien theorem [M.
Martens, W. de Melo and S. van Strien. Julia–Fatou–Sullivan theory for real one-dimensional
dynamics. Acta Math.168(3–4) (1992), 273–318] to hold.
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: O. S.
full_name: KOZLOVSKI, O. S.
last_name: KOZLOVSKI
citation:
ama: Kaloshin V, KOZLOVSKI OS. A Cr unimodal map with an arbitrary fast growth of
the number of periodic points. Ergodic Theory and Dynamical Systems. 2012;32(1):159-165.
doi:10.1017/s0143385710000817
apa: Kaloshin, V., & KOZLOVSKI, O. S. (2012). A Cr unimodal map with an arbitrary
fast growth of the number of periodic points. Ergodic Theory and Dynamical
Systems. Cambridge University Press. https://doi.org/10.1017/s0143385710000817
chicago: Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary
Fast Growth of the Number of Periodic Points.” Ergodic Theory and Dynamical
Systems. Cambridge University Press, 2012. https://doi.org/10.1017/s0143385710000817.
ieee: V. Kaloshin and O. S. KOZLOVSKI, “A Cr unimodal map with an arbitrary fast
growth of the number of periodic points,” Ergodic Theory and Dynamical Systems,
vol. 32, no. 1. Cambridge University Press, pp. 159–165, 2012.
ista: Kaloshin V, KOZLOVSKI OS. 2012. A Cr unimodal map with an arbitrary fast growth
of the number of periodic points. Ergodic Theory and Dynamical Systems. 32(1),
159–165.
mla: Kaloshin, Vadim, and O. S. KOZLOVSKI. “A Cr Unimodal Map with an Arbitrary
Fast Growth of the Number of Periodic Points.” Ergodic Theory and Dynamical
Systems, vol. 32, no. 1, Cambridge University Press, 2012, pp. 159–65, doi:10.1017/s0143385710000817.
short: V. Kaloshin, O.S. KOZLOVSKI, Ergodic Theory and Dynamical Systems 32 (2012)
159–165.
date_created: 2020-09-18T10:47:33Z
date_published: 2012-02-01T00:00:00Z
date_updated: 2021-01-12T08:19:44Z
day: '01'
doi: 10.1017/s0143385710000817
extern: '1'
intvolume: ' 32'
issue: '1'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
month: '02'
oa_version: None
page: 159-165
publication: Ergodic Theory and Dynamical Systems
publication_identifier:
issn:
- 0143-3857
- 1469-4417
publication_status: published
publisher: Cambridge University Press
quality_controlled: '1'
status: public
title: A Cr unimodal map with an arbitrary fast growth of the number of periodic points
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 32
year: '2012'
...
---
_id: '8505'
abstract:
- lang: eng
text: The classical principle of least action says that orbits of mechanical systems
extremize action; an important subclass are those orbits that minimize action.
In this paper we utilize this principle along with Aubry-Mather theory to construct
(Birkhoff) regions of instability for a certain three-body problem, given by a
Hamiltonian system of 2 degrees of freedom. We believe that these methods can
be applied to construct instability regions for a variety of Hamiltonian systems
with 2 degrees of freedom. The Hamiltonian model we consider describes dynamics
of a Sun-Jupiter-comet system, and under some simplifying assumptions, we show
the existence of instabilities for the orbit of the comet. In particular, we show
that a comet which starts close to an orbit in the shape of an ellipse of eccentricity
e=0.66 can increase in eccentricity up to e=0.96. In the sequels to this paper,
we extend the result to beyond e=1 and show the existence of ejection orbits.
Such orbits are initially well within the range of our solar system. This might
give an indication of why most objects rotating around the Sun in our solar system
have relatively low eccentricity.
article_processing_charge: No
article_type: original
author:
- first_name: Joseph
full_name: Galante, Joseph
last_name: Galante
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Galante J, Kaloshin V. Destruction of invariant curves in the restricted circular
planar three-body problem by using comparison of action. Duke Mathematical
Journal. 2011;159(2):275-327. doi:10.1215/00127094-1415878
apa: Galante, J., & Kaloshin, V. (2011). Destruction of invariant curves in
the restricted circular planar three-body problem by using comparison of action.
Duke Mathematical Journal. Duke University Press. https://doi.org/10.1215/00127094-1415878
chicago: Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in
the Restricted Circular Planar Three-Body Problem by Using Comparison of Action.”
Duke Mathematical Journal. Duke University Press, 2011. https://doi.org/10.1215/00127094-1415878.
ieee: J. Galante and V. Kaloshin, “Destruction of invariant curves in the restricted
circular planar three-body problem by using comparison of action,” Duke Mathematical
Journal, vol. 159, no. 2. Duke University Press, pp. 275–327, 2011.
ista: Galante J, Kaloshin V. 2011. Destruction of invariant curves in the restricted
circular planar three-body problem by using comparison of action. Duke Mathematical
Journal. 159(2), 275–327.
mla: Galante, Joseph, and Vadim Kaloshin. “Destruction of Invariant Curves in the
Restricted Circular Planar Three-Body Problem by Using Comparison of Action.”
Duke Mathematical Journal, vol. 159, no. 2, Duke University Press, 2011,
pp. 275–327, doi:10.1215/00127094-1415878.
short: J. Galante, V. Kaloshin, Duke Mathematical Journal 159 (2011) 275–327.
date_created: 2020-09-18T10:47:41Z
date_published: 2011-08-04T00:00:00Z
date_updated: 2021-01-12T08:19:45Z
day: '04'
doi: 10.1215/00127094-1415878
extern: '1'
intvolume: ' 159'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
month: '08'
oa_version: None
page: 275-327
publication: Duke Mathematical Journal
publication_identifier:
issn:
- 0012-7094
publication_status: published
publisher: Duke University Press
quality_controlled: '1'
status: public
title: Destruction of invariant curves in the restricted circular planar three-body
problem by using comparison of action
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 159
year: '2011'
...
---
_id: '8510'
abstract:
- lang: eng
text: In this paper, using the ideas of Bessi and Mather, we present a simple mechanical
system exhibiting Arnold diffusion. This system of a particle in a small periodic
potential can be also interpreted as ray propagation in a periodic optical medium
with a near-constant index of refraction. Arnold diffusion in this context manifests
itself as an arbitrary finite change of direction for nearly constant index of
refraction.
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: Mark
full_name: Levi, Mark
last_name: Levi
citation:
ama: Kaloshin V, Levi M. An example of Arnold diffusion for near-integrable Hamiltonians.
Bulletin of the American Mathematical Society. 2008;45(3):409-427. doi:10.1090/s0273-0979-08-01211-1
apa: Kaloshin, V., & Levi, M. (2008). An example of Arnold diffusion for near-integrable
Hamiltonians. Bulletin of the American Mathematical Society. American Mathematical
Society. https://doi.org/10.1090/s0273-0979-08-01211-1
chicago: Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable
Hamiltonians.” Bulletin of the American Mathematical Society. American
Mathematical Society, 2008. https://doi.org/10.1090/s0273-0979-08-01211-1.
ieee: V. Kaloshin and M. Levi, “An example of Arnold diffusion for near-integrable
Hamiltonians,” Bulletin of the American Mathematical Society, vol. 45,
no. 3. American Mathematical Society, pp. 409–427, 2008.
ista: Kaloshin V, Levi M. 2008. An example of Arnold diffusion for near-integrable
Hamiltonians. Bulletin of the American Mathematical Society. 45(3), 409–427.
mla: Kaloshin, Vadim, and Mark Levi. “An Example of Arnold Diffusion for Near-Integrable
Hamiltonians.” Bulletin of the American Mathematical Society, vol. 45,
no. 3, American Mathematical Society, 2008, pp. 409–27, doi:10.1090/s0273-0979-08-01211-1.
short: V. Kaloshin, M. Levi, Bulletin of the American Mathematical Society 45 (2008)
409–427.
date_created: 2020-09-18T10:48:20Z
date_published: 2008-07-01T00:00:00Z
date_updated: 2021-01-12T08:19:47Z
day: '01'
doi: 10.1090/s0273-0979-08-01211-1
extern: '1'
intvolume: ' 45'
issue: '3'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
month: '07'
oa_version: None
page: 409-427
publication: Bulletin of the American Mathematical Society
publication_identifier:
issn:
- 0273-0979
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: An example of Arnold diffusion for near-integrable Hamiltonians
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 45
year: '2008'
...
---
_id: '8511'
abstract:
- lang: eng
text: "Here we study an amazing phenomenon discovered by Newhouse [S. Newhouse,
Non-density of Axiom A(a) on S2, in: Proc. Sympos. Pure Math., vol. 14, Amer.
Math. Soc., 1970, pp. 191–202; S. Newhouse,\r\nDiffeomorphisms with infinitely
many sinks, Topology 13 (1974) 9–18; S. Newhouse, The abundance of\r\nwild hyperbolic
sets and nonsmooth stable sets of diffeomorphisms, Publ. Math. Inst. Hautes Études
Sci.\r\n50 (1979) 101–151]. It turns out that in the space of Cr smooth diffeomorphisms
Diffr(M) of a compact\r\nsurface M there is an open set U such that a Baire generic
diffeomorphism f ∈ U has infinitely many coexisting sinks. In this paper we make
a step towards understanding “how often does a surface diffeomorphism\r\nhave
infinitely many sinks.” Our main result roughly says that with probability one
for any positive D a\r\nsurface diffeomorphism has only finitely many localized
sinks either of cyclicity bounded by D or those\r\nwhose period is relatively
large compared to its cyclicity. It verifies a particular case of Palis’ Conjecture\r\nsaying
that even though diffeomorphisms with infinitely many coexisting sinks are Baire
generic, they have\r\nprobability zero.\r\nOne of the key points of the proof
is an application of Newton Interpolation Polynomials to study the dynamics initiated
in [V. Kaloshin, B. Hunt, A stretched exponential bound on the rate of growth
of the number\r\nof periodic points for prevalent diffeomorphisms I, Ann. of Math.,
in press, 92 pp.; V. Kaloshin, A stretched\r\nexponential bound on the rate of
growth of the number of periodic points for prevalent diffeomorphisms II,\r\npreprint,
85 pp.]."
article_processing_charge: No
article_type: original
author:
- first_name: A.
full_name: Gorodetski, A.
last_name: Gorodetski
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Gorodetski A, Kaloshin V. How often surface diffeomorphisms have infinitely
many sinks and hyperbolicity of periodic points near a homoclinic tangency. Advances
in Mathematics. 2007;208(2):710-797. doi:10.1016/j.aim.2006.03.012
apa: Gorodetski, A., & Kaloshin, V. (2007). How often surface diffeomorphisms
have infinitely many sinks and hyperbolicity of periodic points near a homoclinic
tangency. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2006.03.012
chicago: Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms
Have Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic
Tangency.” Advances in Mathematics. Elsevier, 2007. https://doi.org/10.1016/j.aim.2006.03.012.
ieee: A. Gorodetski and V. Kaloshin, “How often surface diffeomorphisms have infinitely
many sinks and hyperbolicity of periodic points near a homoclinic tangency,” Advances
in Mathematics, vol. 208, no. 2. Elsevier, pp. 710–797, 2007.
ista: Gorodetski A, Kaloshin V. 2007. How often surface diffeomorphisms have infinitely
many sinks and hyperbolicity of periodic points near a homoclinic tangency. Advances
in Mathematics. 208(2), 710–797.
mla: Gorodetski, A., and Vadim Kaloshin. “How Often Surface Diffeomorphisms Have
Infinitely Many Sinks and Hyperbolicity of Periodic Points near a Homoclinic Tangency.”
Advances in Mathematics, vol. 208, no. 2, Elsevier, 2007, pp. 710–97, doi:10.1016/j.aim.2006.03.012.
short: A. Gorodetski, V. Kaloshin, Advances in Mathematics 208 (2007) 710–797.
date_created: 2020-09-18T10:48:27Z
date_published: 2007-01-30T00:00:00Z
date_updated: 2021-01-12T08:19:47Z
day: '30'
doi: 10.1016/j.aim.2006.03.012
extern: '1'
intvolume: ' 208'
issue: '2'
keyword:
- General Mathematics
language:
- iso: eng
month: '01'
oa_version: None
page: 710-797
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
status: public
title: How often surface diffeomorphisms have infinitely many sinks and hyperbolicity
of periodic points near a homoclinic tangency
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 208
year: '2007'
...
---
_id: '8517'
abstract:
- lang: eng
text: We consider the evolution of a connected set on the plane carried by a space
periodic incompressible stochastic flow. While for almost every realization of
the stochastic flow at time t most of the particles are at a distance of order
equation image away from the origin, there is a measure zero set of points that
escape to infinity at the linear rate. We study the set of points visited by the
original set by time t and show that such a set, when scaled down by the factor
of t, has a limiting nonrandom shape.
article_processing_charge: No
article_type: original
author:
- first_name: Dmitry
full_name: Dolgopyat, Dmitry
last_name: Dolgopyat
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Leonid
full_name: Koralov, Leonid
last_name: Koralov
citation:
ama: Dolgopyat D, Kaloshin V, Koralov L. A limit shape theorem for periodic stochastic
dispersion. Communications on Pure and Applied Mathematics. 2004;57(9):1127-1158.
doi:10.1002/cpa.20032
apa: Dolgopyat, D., Kaloshin, V., & Koralov, L. (2004). A limit shape theorem
for periodic stochastic dispersion. Communications on Pure and Applied Mathematics.
Wiley. https://doi.org/10.1002/cpa.20032
chicago: Dolgopyat, Dmitry, Vadim Kaloshin, and Leonid Koralov. “A Limit Shape Theorem
for Periodic Stochastic Dispersion.” Communications on Pure and Applied Mathematics.
Wiley, 2004. https://doi.org/10.1002/cpa.20032.
ieee: D. Dolgopyat, V. Kaloshin, and L. Koralov, “A limit shape theorem for periodic
stochastic dispersion,” Communications on Pure and Applied Mathematics,
vol. 57, no. 9. Wiley, pp. 1127–1158, 2004.
ista: Dolgopyat D, Kaloshin V, Koralov L. 2004. A limit shape theorem for periodic
stochastic dispersion. Communications on Pure and Applied Mathematics. 57(9),
1127–1158.
mla: Dolgopyat, Dmitry, et al. “A Limit Shape Theorem for Periodic Stochastic Dispersion.”
Communications on Pure and Applied Mathematics, vol. 57, no. 9, Wiley,
2004, pp. 1127–58, doi:10.1002/cpa.20032.
short: D. Dolgopyat, V. Kaloshin, L. Koralov, Communications on Pure and Applied
Mathematics 57 (2004) 1127–1158.
date_created: 2020-09-18T10:49:12Z
date_published: 2004-09-01T00:00:00Z
date_updated: 2021-01-12T08:19:50Z
day: '01'
doi: 10.1002/cpa.20032
extern: '1'
intvolume: ' 57'
issue: '9'
keyword:
- Applied Mathematics
- General Mathematics
language:
- iso: eng
month: '09'
oa_version: None
page: 1127-1158
publication: Communications on Pure and Applied Mathematics
publication_identifier:
issn:
- 0010-3640
- 1097-0312
publication_status: published
publisher: Wiley
quality_controlled: '1'
status: public
title: A limit shape theorem for periodic stochastic dispersion
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 57
year: '2004'
...
---
_id: '8519'
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. The existential Hilbert 16-th problem and an estimate for cyclicity
of elementary polycycles. Inventiones mathematicae. 2003;151(3):451-512.
doi:10.1007/s00222-002-0244-9
apa: Kaloshin, V. (2003). The existential Hilbert 16-th problem and an estimate
for cyclicity of elementary polycycles. Inventiones Mathematicae. Springer
Nature. https://doi.org/10.1007/s00222-002-0244-9
chicago: Kaloshin, Vadim. “The Existential Hilbert 16-Th Problem and an Estimate
for Cyclicity of Elementary Polycycles.” Inventiones Mathematicae. Springer
Nature, 2003. https://doi.org/10.1007/s00222-002-0244-9.
ieee: V. Kaloshin, “The existential Hilbert 16-th problem and an estimate for cyclicity
of elementary polycycles,” Inventiones mathematicae, vol. 151, no. 3. Springer
Nature, pp. 451–512, 2003.
ista: Kaloshin V. 2003. The existential Hilbert 16-th problem and an estimate for
cyclicity of elementary polycycles. Inventiones mathematicae. 151(3), 451–512.
mla: Kaloshin, Vadim. “The Existential Hilbert 16-Th Problem and an Estimate for
Cyclicity of Elementary Polycycles.” Inventiones Mathematicae, vol. 151,
no. 3, Springer Nature, 2003, pp. 451–512, doi:10.1007/s00222-002-0244-9.
short: V. Kaloshin, Inventiones Mathematicae 151 (2003) 451–512.
date_created: 2020-09-18T10:49:26Z
date_published: 2003-03-01T00:00:00Z
date_updated: 2021-01-12T08:19:50Z
day: '01'
doi: 10.1007/s00222-002-0244-9
extern: '1'
intvolume: ' 151'
issue: '3'
keyword:
- General Mathematics
language:
- iso: eng
month: '03'
oa_version: None
page: 451-512
publication: Inventiones mathematicae
publication_identifier:
issn:
- 0020-9910
- 1432-1297
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
status: public
title: The existential Hilbert 16-th problem and an estimate for cyclicity of elementary
polycycles
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 151
year: '2003'
...
---
_id: '8521'
abstract:
- lang: eng
text: We continue the previous article's discussion of bounds, for prevalent diffeomorphisms
of smooth compact manifolds, on the growth of the number of periodic points and
the decay of their hyperbolicity as a function of their period $n$. In that article
we reduced the main results to a problem, for certain families of diffeomorphisms,
of bounding the measure of parameter values for which the diffeomorphism has (for
a given period $n$) an almost periodic point that is almost nonhyperbolic. We
also formulated our results for $1$-dimensional endomorphisms on a compact interval.
In this article we describe some of the main techniques involved and outline the
rest of the proof. To simplify notation, we concentrate primarily on the $1$-dimensional
case.
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: Brian R.
full_name: Hunt, Brian R.
last_name: Hunt
citation:
ama: Kaloshin V, Hunt BR. A stretched exponential bound on the rate of growth of
the number of periodic points for prevalent diffeomorphisms II. Electronic
Research Announcements of the American Mathematical Society. 2001;7(5):28-36.
doi:10.1090/s1079-6762-01-00091-9
apa: Kaloshin, V., & Hunt, B. R. (2001). A stretched exponential bound on the
rate of growth of the number of periodic points for prevalent diffeomorphisms
II. Electronic Research Announcements of the American Mathematical Society.
American Mathematical Society. https://doi.org/10.1090/s1079-6762-01-00091-9
chicago: Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the
Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms
II.” Electronic Research Announcements of the American Mathematical Society.
American Mathematical Society, 2001. https://doi.org/10.1090/s1079-6762-01-00091-9.
ieee: V. Kaloshin and B. R. Hunt, “A stretched exponential bound on the rate of
growth of the number of periodic points for prevalent diffeomorphisms II,” Electronic
Research Announcements of the American Mathematical Society, vol. 7, no. 5.
American Mathematical Society, pp. 28–36, 2001.
ista: Kaloshin V, Hunt BR. 2001. A stretched exponential bound on the rate of growth
of the number of periodic points for prevalent diffeomorphisms II. Electronic
Research Announcements of the American Mathematical Society. 7(5), 28–36.
mla: Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate
of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms II.”
Electronic Research Announcements of the American Mathematical Society,
vol. 7, no. 5, American Mathematical Society, 2001, pp. 28–36, doi:10.1090/s1079-6762-01-00091-9.
short: V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American
Mathematical Society 7 (2001) 28–36.
date_created: 2020-09-18T10:49:43Z
date_published: 2001-04-24T00:00:00Z
date_updated: 2021-01-12T08:19:51Z
day: '24'
doi: 10.1090/s1079-6762-01-00091-9
extern: '1'
intvolume: ' 7'
issue: '5'
keyword:
- General Mathematics
language:
- iso: eng
month: '04'
oa_version: None
page: 28-36
publication: Electronic Research Announcements of the American Mathematical Society
publication_identifier:
issn:
- 1079-6762
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: A stretched exponential bound on the rate of growth of the number of periodic
points for prevalent diffeomorphisms II
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2001'
...
---
_id: '8522'
abstract:
- lang: eng
text: For diffeomorphisms of smooth compact manifolds, we consider the problem of
how fast the number of periodic points with period $n$grows as a function of $n$.
In many familiar cases (e.g., Anosov systems) the growth is exponential, but arbitrarily
fast growth is possible; in fact, the first author has shown that arbitrarily
fast growth is topologically (Baire) generic for $C^2$ or smoother diffeomorphisms.
In the present work we show that, by contrast, for a measure-theoretic notion
of genericity we call ``prevalence'', the growth is not much faster than exponential.
Specifically, we show that for each $\delta > 0$, there is a prevalent set of
( $C^{1+\rho}$ or smoother) diffeomorphisms for which the number of period $n$
points is bounded above by $\operatorname{exp}(C n^{1+\delta})$ for some $C$ independent
of $n$. We also obtain a related bound on the decay of the hyperbolicity of the
periodic points as a function of $n$. The contrast between topologically generic
and measure-theoretically generic behavior for the growth of the number of periodic
points and the decay of their hyperbolicity shows this to be a subtle and complex
phenomenon, reminiscent of KAM theory.
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: Brian R.
full_name: Hunt, Brian R.
last_name: Hunt
citation:
ama: Kaloshin V, Hunt BR. A stretched exponential bound on the rate of growth of
the number of periodic points for prevalent diffeomorphisms I. Electronic Research
Announcements of the American Mathematical Society. 2001;7(4):17-27. doi:10.1090/s1079-6762-01-00090-7
apa: Kaloshin, V., & Hunt, B. R. (2001). A stretched exponential bound on the
rate of growth of the number of periodic points for prevalent diffeomorphisms
I. Electronic Research Announcements of the American Mathematical Society.
American Mathematical Society. https://doi.org/10.1090/s1079-6762-01-00090-7
chicago: Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the
Rate of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms
I.” Electronic Research Announcements of the American Mathematical Society.
American Mathematical Society, 2001. https://doi.org/10.1090/s1079-6762-01-00090-7.
ieee: V. Kaloshin and B. R. Hunt, “A stretched exponential bound on the rate of
growth of the number of periodic points for prevalent diffeomorphisms I,” Electronic
Research Announcements of the American Mathematical Society, vol. 7, no. 4.
American Mathematical Society, pp. 17–27, 2001.
ista: Kaloshin V, Hunt BR. 2001. A stretched exponential bound on the rate of growth
of the number of periodic points for prevalent diffeomorphisms I. Electronic Research
Announcements of the American Mathematical Society. 7(4), 17–27.
mla: Kaloshin, Vadim, and Brian R. Hunt. “A Stretched Exponential Bound on the Rate
of Growth of the Number of Periodic Points for Prevalent Diffeomorphisms I.” Electronic
Research Announcements of the American Mathematical Society, vol. 7, no. 4,
American Mathematical Society, 2001, pp. 17–27, doi:10.1090/s1079-6762-01-00090-7.
short: V. Kaloshin, B.R. Hunt, Electronic Research Announcements of the American
Mathematical Society 7 (2001) 17–27.
date_created: 2020-09-18T10:49:56Z
date_published: 2001-04-18T00:00:00Z
date_updated: 2021-01-12T08:19:51Z
day: '18'
doi: 10.1090/s1079-6762-01-00090-7
extern: '1'
intvolume: ' 7'
issue: '4'
keyword:
- General Mathematics
language:
- iso: eng
month: '04'
oa_version: None
page: 17-27
publication: Electronic Research Announcements of the American Mathematical Society
publication_identifier:
issn:
- 1079-6762
publication_status: published
publisher: American Mathematical Society
quality_controlled: '1'
status: public
title: A stretched exponential bound on the rate of growth of the number of periodic
points for prevalent diffeomorphisms I
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 7
year: '2001'
...