---
OA_place: publisher
_id: '22255'
abstract:
- lang: eng
text: "This thesis studies spectral rigidity and nonrigidity phenomena in dynamical
systems. The central question is whether a dynamical system can be determined,
up to a natural conjugacy, from its spectrum. We consider three related spectra:
the length spectrum, the action spectrum, and the Lyapunov spectrum.\r\n\r\nThe
first part of the thesis concerns Liouville metrics on the two-dimensional torus.
It is a long-standing folklore conjecture that Liouville metrics are the only
integrable metrics on the torus. We prove a length-spectral rigidity result for
linear conformal deformations of Liouville metrics by exploiting the dynamical
properties of the rational tori -- analogues of the resonant convex caustics in
billiards. We also establish a complementary classification result showing that
marked-length-isospectral Liouville metrics are characterized by rearrangements
of the one-dimensional functions appearing in their conformal factors, generalizing
a theorem of Abbondandolo-Mazzucchelli. In particular, the second result gives
nonrigidity examples within the class of Liouville metrics.\r\n\r\nThe second
part of the thesis studies the standard map from the viewpoint of action and Lyapunov
spectra. We construct nontrivial deformations of the standard map which preserve
the symplectic actions (respectively, the Lyapunov exponents) of infinitely many
periodic orbits accumulating on an invariant curve. The proof combines a resonant
normal form construction with Picard iteration schemes to obtain a sequence of
periodic orbits accumulating on an invariant curve with a Liouville rotation number.
Within the resonant normal forms we capture the dependence of these periodic orbits
on the resonant Fourier coefficients of the dynamics on the invariant curve and,
using the contraction mapping principle, obtain a suitable deformation achieving
the prescribed spectral data associated with this sequence of orbits. The result
can be viewed as a symplectic twist-map analogue of a length-spectral nonrigidity
phenomenon for Riemannian manifolds and convex billiards, and it motivates the
existence problem for similar 'partially length-isospectral' deformations of strictly
convex billiard tables.\r\n"
acknowledged_ssus:
- _id: E-Lib
- _id: CampIT
acknowledgement: "The financial support of the ERC grant SPERIG #885707 is gratefully
acknowledged.\r\n"
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Yunzhe
full_name: Li, Yunzhe
id: 41cb05d3-f128-11eb-9611-e4e2b3cfba31
last_name: Li
citation:
ama: Li Y. Spectral rigidity and nonrigidity of dynamical systems. 2026. doi:10.15479/AT-ISTA-22255
apa: Li, Y. (2026). Spectral rigidity and nonrigidity of dynamical systems.
Institute of Science and Technology Austria. https://doi.org/10.15479/AT-ISTA-22255
chicago: Li, Yunzhe. “Spectral Rigidity and Nonrigidity of Dynamical Systems.” Institute
of Science and Technology Austria, 2026. https://doi.org/10.15479/AT-ISTA-22255.
ieee: Y. Li, “Spectral rigidity and nonrigidity of dynamical systems,” Institute
of Science and Technology Austria, 2026.
ista: Li Y. 2026. Spectral rigidity and nonrigidity of dynamical systems. Institute
of Science and Technology Austria.
mla: Li, Yunzhe. Spectral Rigidity and Nonrigidity of Dynamical Systems.
Institute of Science and Technology Austria, 2026, doi:10.15479/AT-ISTA-22255.
short: Y. Li, Spectral Rigidity and Nonrigidity of Dynamical Systems, Institute
of Science and Technology Austria, 2026.
corr_author: '1'
date_created: 2026-07-08T12:44:31Z
date_published: 2026-07-11T00:00:00Z
date_updated: 2026-07-20T14:58:23Z
day: '11'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: VaKa
doi: 10.15479/AT-ISTA-22255
doi_confirm: '1'
ec_funded: 1
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oa: 1
oa_version: Published Version
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call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
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status: public
supervisor:
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
title: Spectral rigidity and nonrigidity of dynamical systems
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: dissertation
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '14278'
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 almost every ellipse
that preserves integrability near the boundary, is itself an ellipse. We apply
this result to study local spectral uniqueness of ellipses using the connection
between the wave trace of the Laplacian and the dynamics near the boundary and
establish local uniqueness for almost all of them.'
acknowledgement: 'The author acknowledges the partial support of the European Research
Council Grant #885707. He also thanks Vadim Kaloshin for proposing the idea of the
project and greatly aiding the implementation. The author is also grateful to Hamid
Hezari, Amir Vig, Steve Zelditch, Comlan E. Koudjinan, Corentin Fierobe, Ngo Nhok
Tkhai Shon and Roman Sarapin for useful discussions. The author also acknowledges
partial support of ISTern summer program. The project started in the summer of 2021,
when the author was an intern at ISTA. Open access funding provided by Institute
of Science and Technology (IST Austria).'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Illya
full_name: Koval, Illya
id: 2eed1f3b-896a-11ed-bdf8-93c7c4bf159e
last_name: Koval
citation:
ama: Koval I. Local strong Birkhoff conjecture and local spectral rigidity of almost
every ellipse. Inventiones Mathematicae. 2026;244:221-298. doi:10.1007/s00222-025-01397-y
apa: Koval, I. (2026). Local strong Birkhoff conjecture and local spectral rigidity
of almost every ellipse. Inventiones Mathematicae. Springer Nature. https://doi.org/10.1007/s00222-025-01397-y
chicago: Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity
of Almost Every Ellipse.” Inventiones Mathematicae. Springer Nature, 2026.
https://doi.org/10.1007/s00222-025-01397-y.
ieee: I. Koval, “Local strong Birkhoff conjecture and local spectral rigidity of
almost every ellipse,” Inventiones Mathematicae, vol. 244. Springer Nature,
pp. 221–298, 2026.
ista: Koval I. 2026. Local strong Birkhoff conjecture and local spectral rigidity
of almost every ellipse. Inventiones Mathematicae. 244, 221–298.
mla: Koval, Illya. “Local Strong Birkhoff Conjecture and Local Spectral Rigidity
of Almost Every Ellipse.” Inventiones Mathematicae, vol. 244, Springer
Nature, 2026, pp. 221–98, doi:10.1007/s00222-025-01397-y.
short: I. Koval, Inventiones Mathematicae 244 (2026) 221–298.
corr_author: '1'
das_tickbox: '0'
date_created: 2023-09-06T08:35:43Z
date_published: 2026-04-01T00:00:00Z
date_updated: 2026-07-23T10:58:59Z
day: '01'
ddc:
- '510'
department:
- _id: GradSch
- _id: VaKa
doi: 10.1007/s00222-025-01397-y
ec_funded: 1
external_id:
arxiv:
- '2111.12171'
file:
- access_level: open_access
checksum: 487fa9113e1bbf32a6c70e6d1e8f63bc
content_type: application/pdf
creator: dernst
date_created: 2026-07-23T10:55:24Z
date_updated: 2026-07-23T10:55:24Z
file_id: '22394'
file_name: 2026_InventionesMath_Koval.pdf
file_size: 2256345
relation: main_file
success: 1
file_date_updated: 2026-07-23T10:55:24Z
fulldoi: https://doi.org/10.1007/s00222-025-01397-y
has_accepted_license: '1'
intvolume: ' 244'
language:
- iso: eng
mathsc:
- 37C83
- 35J05
- 37J70
- 74J25
month: '04'
oa: 1
oa_version: Published Version
page: 221-298
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'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
title: Local strong Birkhoff conjecture and local spectral rigidity of almost every
ellipse
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 244
year: '2026'
...
---
DOAJ_listed: '1'
OA_place: publisher
OA_type: gold
_id: '20839'
abstract:
- lang: eng
text: For every couple of Hausdorff functions ψ and φ verifying some mild assumptions,
there exists a compact subset K of the Baire space such that the φ-Hausdorff measure
and the ψ-packing measure on K are both finite and positive. Such examples are
then embedded in any infinite dimensional Banach space to answer positively a
question of Fan on the existence of metric spaces with arbitrary scales.
article_processing_charge: Yes
article_type: original
author:
- first_name: Mathieu
full_name: Helfter, Mathieu
id: 7d296fbe-e2c6-11ee-84d3-d5c2945f9a57
last_name: Helfter
citation:
ama: Helfter M. Sets with arbitrary Hausdorff and packing scales in infinite dimensional
Banach spaces. Journal of Fractal Geometry. 2025. doi:10.4171/jfg/177
apa: Helfter, M. (2025). Sets with arbitrary Hausdorff and packing scales in infinite
dimensional Banach spaces. Journal of Fractal Geometry. EMS Press. https://doi.org/10.4171/jfg/177
chicago: Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in
Infinite Dimensional Banach Spaces.” Journal of Fractal Geometry. EMS Press,
2025. https://doi.org/10.4171/jfg/177.
ieee: M. Helfter, “Sets with arbitrary Hausdorff and packing scales in infinite
dimensional Banach spaces,” Journal of Fractal Geometry. EMS Press, 2025.
ista: Helfter M. 2025. Sets with arbitrary Hausdorff and packing scales in infinite
dimensional Banach spaces. Journal of Fractal Geometry.
mla: Helfter, Mathieu. “Sets with Arbitrary Hausdorff and Packing Scales in Infinite
Dimensional Banach Spaces.” Journal of Fractal Geometry, EMS Press, 2025,
doi:10.4171/jfg/177.
short: M. Helfter, Journal of Fractal Geometry (2025).
corr_author: '1'
date_created: 2025-12-19T10:15:37Z
date_published: 2025-11-07T00:00:00Z
date_updated: 2026-06-18T18:26:33Z
day: '07'
ddc:
- '500'
department:
- _id: VaKa
doi: 10.4171/jfg/177
fulldoi: https://doi.org/10.4171/jfg/177
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.4171/jfg/177
month: '11'
oa: 1
oa_version: Published Version
publication: Journal of Fractal Geometry
publication_identifier:
eissn:
- 2308-1317
issn:
- 2308-1309
publication_status: epub_ahead
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Sets with arbitrary Hausdorff and packing scales in infinite dimensional Banach
spaces
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '19496'
abstract:
- lang: eng
text: We introduce the notions of scale for sets and measures on metric space by
generalizing the usual notions of dimension. Several versions of scales are introduced
such as Hausdorff, packing, box, local and quantization. They are defined for
different growth, allowing a refined study of infinite dimensional spaces. We
prove general theorems comparing the different versions of scales. They are applied
to describe geometries of ergodic decompositions, of the Wiener measure and from
functional spaces. The first application solves a problem of Berger on the notions
of emergence (2020); the second lies in the geometry of the Wiener measure and
extends the work of Dereich–Lifshits (2005); the last refines Kolmogorov–Tikhomirov
(1958) study on finitely differentiable functions.
article_number: '15'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Mathieu
full_name: Helfter, Mathieu
id: 7d296fbe-e2c6-11ee-84d3-d5c2945f9a57
last_name: Helfter
citation:
ama: Helfter M. Scales. Mathematische Zeitschrift. 2025;310. doi:10.1007/s00209-025-03719-5
apa: Helfter, M. (2025). Scales. Mathematische Zeitschrift. Springer Nature.
https://doi.org/10.1007/s00209-025-03719-5
chicago: Helfter, Mathieu. “Scales.” Mathematische Zeitschrift. Springer
Nature, 2025. https://doi.org/10.1007/s00209-025-03719-5.
ieee: M. Helfter, “Scales,” Mathematische Zeitschrift, vol. 310. Springer
Nature, 2025.
ista: Helfter M. 2025. Scales. Mathematische Zeitschrift. 310, 15.
mla: Helfter, Mathieu. “Scales.” Mathematische Zeitschrift, vol. 310, 15,
Springer Nature, 2025, doi:10.1007/s00209-025-03719-5.
short: M. Helfter, Mathematische Zeitschrift 310 (2025).
corr_author: '1'
date_created: 2025-04-06T22:01:32Z
date_published: 2025-05-01T00:00:00Z
date_updated: 2025-09-30T11:31:00Z
day: '01'
department:
- _id: VaKa
doi: 10.1007/s00209-025-03719-5
external_id:
arxiv:
- '2206.05231'
isi:
- '001450830300001'
fulldoi: https://doi.org/10.1007/s00209-025-03719-5
intvolume: ' 310'
isi: 1
language:
- iso: eng
main_file_link:
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month: '05'
oa: 1
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publication: Mathematische Zeitschrift
publication_identifier:
eissn:
- 1432-1823
issn:
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publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Scales
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 310
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '20185'
abstract:
- lang: eng
text: We show a local rigidity result for the integrability of symplectic billiards.
We prove that any domain which is close to an ellipse, and for which the symplectic
billiard map is rationally integrable must be an ellipse as well. This is in spirit
of the result of [2] for Birkhoff billiards.
acknowledgement: The author would like to thank Corentin Fierobe, Vadim Kaloshin,
Illya Koval and Yunzhe Li for useful discussions. The author would also like to
thank the referee for useful remarks. Open access funding provided by Institute
of Science and Technology (IST Austria). European Research Council (885707) Mr Daniel
Tsodikovich
article_number: '306'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Daniel
full_name: Tsodikovich, Daniel
id: 04531810-fb3e-11ef-87f0-800a4ce333db
last_name: Tsodikovich
citation:
ama: Tsodikovich D. Local rigidity for symplectic billiards. Journal of Geometric
Analysis. 2025;35(10). doi:10.1007/s12220-025-02148-4
apa: Tsodikovich, D. (2025). Local rigidity for symplectic billiards. Journal
of Geometric Analysis. Springer Nature. https://doi.org/10.1007/s12220-025-02148-4
chicago: Tsodikovich, Daniel. “Local Rigidity for Symplectic Billiards.” Journal
of Geometric Analysis. Springer Nature, 2025. https://doi.org/10.1007/s12220-025-02148-4.
ieee: D. Tsodikovich, “Local rigidity for symplectic billiards,” Journal of Geometric
Analysis, vol. 35, no. 10. Springer Nature, 2025.
ista: Tsodikovich D. 2025. Local rigidity for symplectic billiards. Journal of Geometric
Analysis. 35(10), 306.
mla: Tsodikovich, Daniel. “Local Rigidity for Symplectic Billiards.” Journal
of Geometric Analysis, vol. 35, no. 10, 306, Springer Nature, 2025, doi:10.1007/s12220-025-02148-4.
short: D. Tsodikovich, Journal of Geometric Analysis 35 (2025).
corr_author: '1'
date_created: 2025-08-17T22:01:35Z
date_published: 2025-08-07T00:00:00Z
date_updated: 2025-12-30T09:29:27Z
day: '07'
ddc:
- '510'
department:
- _id: VaKa
doi: 10.1007/s12220-025-02148-4
ec_funded: 1
external_id:
arxiv:
- '2501.08849'
isi:
- '001546433200002'
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creator: dernst
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month: '08'
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oa_version: Published Version
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Journal of Geometric Analysis
publication_identifier:
issn:
- 1050-6926
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Local rigidity for symplectic billiards
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 35
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22340'
abstract:
- lang: eng
text: We show that Laplace isospectral deformations within a conformal class of
generic Liouville metrics on the two-dimensional torus that are linear in the
deformation parameter are necessarily trivial. Two of the main ingredients in
our proof are a noncancellation result for the wave trace and an analysis of the
second order variational formula for the energy functional associated to closed
geodesics. Noncancellation allows us to detect parts of the length spectrum from
the Laplace spectrum and conclude rational integrability for the deformed geodesic
flow (Liouville metrics are folklorically conjectured to be the only Riemannian
metrics with integrable geodesic flow on the torus). We then use the second variational
formula to show how the preservation of a single rational torus is sufficient
to conclude triviality of the deformation, assuming linearity. We also present
some evidence that our hypothesis of linearity may indeed be necessary.
article_processing_charge: No
arxiv: 1
author:
- first_name: Sven Joscha
full_name: Henheik, Sven Joscha
id: 31d731d7-d235-11ea-ad11-b50331c8d7fb
last_name: Henheik
orcid: 0000-0003-1106-327X
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
- first_name: Yunzhe
full_name: Li, Yunzhe
id: 41cb05d3-f128-11eb-9611-e4e2b3cfba31
last_name: Li
- first_name: Amir
full_name: Vig, Amir
id: 49d58dd5-45f5-11ec-9f86-8ce1276989b9
last_name: Vig
citation:
ama: Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori. arXiv.
doi:10.48550/ARXIV.2511.10398
apa: Henheik, S. J., Kaloshin, V., Li, Y., & Vig, A. (n.d.). Spectral rigidity
of Liouville tori. arXiv. https://doi.org/10.48550/ARXIV.2511.10398
chicago: Henheik, Sven Joscha, Vadim Kaloshin, Yunzhe Li, and Amir Vig. “Spectral
Rigidity of Liouville Tori.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2511.10398.
ieee: S. J. Henheik, V. Kaloshin, Y. Li, and A. Vig, “Spectral rigidity of Liouville
tori,” arXiv. .
ista: Henheik SJ, Kaloshin V, Li Y, Vig A. Spectral rigidity of Liouville tori.
arXiv, 10.48550/ARXIV.2511.10398.
mla: Henheik, Sven Joscha, et al. “Spectral Rigidity of Liouville Tori.” ArXiv,
doi:10.48550/ARXIV.2511.10398.
short: S.J. Henheik, V. Kaloshin, Y. Li, A. Vig, ArXiv (n.d.).
corr_author: '1'
date_created: 2026-07-14T12:51:50Z
date_published: 2025-11-13T00:00:00Z
date_updated: 2026-07-20T14:58:23Z
day: '13'
department:
- _id: VaKa
- _id: LaEr
doi: 10.48550/ARXIV.2511.10398
external_id:
arxiv:
- '2511.10398'
fulldoi: https://doi.org/10.48550/ARXIV.2511.10398
keyword:
- Differential Geometry (math.DG)
- Mathematical Physics (math-ph)
- Dynamical Systems (math.DS)
- Spectral Theory (math.SP)
- 'FOS: Mathematics'
- 'FOS: Mathematics'
- 'FOS: Physical sciences'
- 'FOS: Physical sciences'
- 58J42
- 37J35
- 37J35
- 35P20
- 58J40
- 58J50
- 37D40
language:
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main_file_link:
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url: https://doi.org/10.48550/arXiv.2511.10398
month: '11'
oa: 1
oa_version: Preprint
publication: arXiv
publication_status: draft
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status: public
status: public
title: Spectral rigidity of Liouville tori
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: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '22341'
abstract:
- lang: eng
text: We construct nontrivial deformations of the standard map which preserve the
symplectic actions, respectively the Lyapunov exponents, of infinitely many periodic
orbits accumulating to an invariant curve. The proof uses a resonant normal-form
construction to obtain a sequence of periodic orbits accumulating on an invariant
curve with a Liouville rotation number. Within these normal forms we capture the
dependence of these periodic orbits on the resonant Fourier coefficients of the
dynamics on the invariant curve and, using the contraction mapping principle,
obtain a suitable deformation achieving the prescribed spectral data associated
with this sequence of orbits. The result can be viewed as a symplectic twist-map
analogue of a length spectral nonrigidity phenomenon for Riemannian manifolds
and convex billiards, and it motivates the existence problem for similar 'partially
length-isospectral' deformations of strictly convex billiard tables.
acknowledgement: " The author would like to thank Vadim Kaloshin for initiating this
project and for his guidance throughout its development. The author also\r\nthanks
Abed Bounemoura, Bassam Fayad, Mathieu Helfter, Comlan Edmond Koudjinan, Illya Koval,
Yi Pan, and Daniel Tsodikovich for many helpful discussions. The\r\nfinancial support
of the ERC grant SPERIG #885707 is gratefully acknowledged."
article_processing_charge: No
arxiv: 1
author:
- first_name: Yunzhe
full_name: Li, Yunzhe
id: 41cb05d3-f128-11eb-9611-e4e2b3cfba31
last_name: Li
citation:
ama: Li Y. Deformations of the standard map with prescribed actions and Lyapunov
exponents. arXiv. doi:10.48550/ARXIV.2512.03865
apa: Li, Y. (n.d.). Deformations of the standard map with prescribed actions and
Lyapunov exponents. arXiv. https://doi.org/10.48550/ARXIV.2512.03865
chicago: Li, Yunzhe. “Deformations of the Standard Map with Prescribed Actions and
Lyapunov Exponents.” ArXiv, n.d. https://doi.org/10.48550/ARXIV.2512.03865.
ieee: Y. Li, “Deformations of the standard map with prescribed actions and Lyapunov
exponents,” arXiv. .
ista: Li Y. Deformations of the standard map with prescribed actions and Lyapunov
exponents. arXiv, 10.48550/ARXIV.2512.03865.
mla: Li, Yunzhe. “Deformations of the Standard Map with Prescribed Actions and Lyapunov
Exponents.” ArXiv, doi:10.48550/ARXIV.2512.03865.
short: Y. Li, ArXiv (n.d.).
corr_author: '1'
date_created: 2026-07-14T13:02:29Z
date_published: 2025-12-03T00:00:00Z
date_updated: 2026-07-20T14:58:23Z
day: '03'
department:
- _id: VaKa
doi: 10.48550/ARXIV.2512.03865
ec_funded: 1
external_id:
arxiv:
- '2512.03865'
fulldoi: https://doi.org/10.48550/ARXIV.2512.03865
keyword:
- Dynamical Systems (math.DS)
- 'FOS: Mathematics'
- 'FOS: Mathematics'
language:
- iso: eng
main_file_link:
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url: https://doi.org/10.48550/arXiv.2512.03865
month: '12'
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: arXiv
publication_status: draft
related_material:
record:
- id: '22255'
relation: dissertation_contains
status: public
status: public
title: Deformations of the standard map with prescribed actions and Lyapunov exponents
type: preprint
user_id: 8b945eb4-e2f2-11eb-945a-df72226e66a9
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18483'
abstract:
- lang: eng
text: In this paper we prove a perturbative version of a remarkable Bialy–Mironov
(Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff
conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric
convex domain with integrable billiard is ellipse. We combine techniques from
Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino
(Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally
symmetric one with integrable billiard is ellipse. To combine these results we
derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by
proving that a notion of rational integrability is equivalent to the C0-integrability
condition used in their paper.
acknowledgement: We are grateful to the anonymous referee for their careful reading
and valuable remarks and comments which helped to improve significantly the paper.
Open access funding provided by Institute of Science and Technology (IST Austria).
V.K. and C.E.K. gratefully acknowledge support from the European Research Council
(ERC) through the Advanced Grant “SPERIG” (#885 707).
article_processing_charge: Yes (via OA deal)
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: Edmond
full_name: Koudjinan, Edmond
id: 52DF3E68-AEFA-11EA-95A4-124A3DDC885E
last_name: Koudjinan
orcid: 0000-0003-2640-4049
- first_name: Ke
full_name: Zhang, Ke
last_name: Zhang
citation:
ama: Kaloshin V, Koudjinan E, Zhang K. Birkhoff conjecture for nearly centrally
symmetric domains. Geometric and Functional Analysis. 2024;34:1973-2007.
doi:10.1007/s00039-024-00695-6
apa: Kaloshin, V., Koudjinan, E., & Zhang, K. (2024). Birkhoff conjecture for
nearly centrally symmetric domains. Geometric and Functional Analysis.
Springer Nature. https://doi.org/10.1007/s00039-024-00695-6
chicago: Kaloshin, Vadim, Edmond Koudjinan, and Ke Zhang. “Birkhoff Conjecture for
Nearly Centrally Symmetric Domains.” Geometric and Functional Analysis.
Springer Nature, 2024. https://doi.org/10.1007/s00039-024-00695-6.
ieee: V. Kaloshin, E. Koudjinan, and K. Zhang, “Birkhoff conjecture for nearly centrally
symmetric domains,” Geometric and Functional Analysis, vol. 34. Springer
Nature, pp. 1973–2007, 2024.
ista: Kaloshin V, Koudjinan E, Zhang K. 2024. Birkhoff conjecture for nearly centrally
symmetric domains. Geometric and Functional Analysis. 34, 1973–2007.
mla: Kaloshin, Vadim, et al. “Birkhoff Conjecture for Nearly Centrally Symmetric
Domains.” Geometric and Functional Analysis, vol. 34, Springer Nature,
2024, pp. 1973–2007, doi:10.1007/s00039-024-00695-6.
short: V. Kaloshin, E. Koudjinan, K. Zhang, Geometric and Functional Analysis 34
(2024) 1973–2007.
corr_author: '1'
date_created: 2024-10-27T23:01:45Z
date_published: 2024-12-01T00:00:00Z
date_updated: 2025-09-08T14:27:45Z
day: '01'
ddc:
- '510'
department:
- _id: VaKa
doi: 10.1007/s00039-024-00695-6
ec_funded: 1
external_id:
arxiv:
- '2306.12301'
isi:
- '001329804200001'
file:
- access_level: open_access
checksum: e7fcd9f78beb40408c7d858ac0625e27
content_type: application/pdf
creator: dernst
date_created: 2025-01-13T09:14:24Z
date_updated: 2025-01-13T09:14:24Z
file_id: '18833'
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file_size: 2260980
relation: main_file
success: 1
file_date_updated: 2025-01-13T09:14:24Z
fulldoi: https://doi.org/10.1007/s00039-024-00695-6
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intvolume: ' 34'
isi: 1
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
page: 1973-2007
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Geometric and Functional Analysis
publication_identifier:
eissn:
- 1420-8970
issn:
- 1016-443X
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Birkhoff conjecture for nearly centrally symmetric domains
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 34
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '18586'
abstract:
- lang: eng
text: "We prove the Central Limit Theorem and superpolynomial mixing for environment\r\nviewed
from the particle process in quasi periodic Diophantine random environment. The
main\r\ningredients are smoothness estimates for the solution of the Poisson equation
and local limit asymptotics for certain accelerated walks."
acknowledgement: "ents. The authors are grateful to Agnieszka Zelerowicz and the anonymous
referee\r\nfor useful comments. The first author is grateful to Minsung Kim for
providing some references.\r\nThe first author has been supported by the European
Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie
Grant Agreement No. 101034413. The second author has been supported by the NSF grant
DMS 2246983."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Klaudiusz S
full_name: Czudek, Klaudiusz S
id: 5c0e116e-803f-11ed-ab7e-90d572405f20
last_name: Czudek
- first_name: Dmitry
full_name: Dolgopyat, Dmitry
last_name: Dolgopyat
citation:
ama: CZUDEK KS, Dolgopyat D. The central limit theorem and rate of mixing for simple
random walks on the circle. Alea. 2024;21(2):1853-1865. doi:10.30757/ALEA.V21-70
apa: CZUDEK, K. S., & Dolgopyat, D. (2024). The central limit theorem and rate
of mixing for simple random walks on the circle. Alea. Instituto Nacional
de Matematica Pura e Aplicada. https://doi.org/10.30757/ALEA.V21-70
chicago: CZUDEK, Klaudiusz S, and Dmitry Dolgopyat. “The Central Limit Theorem and
Rate of Mixing for Simple Random Walks on the Circle.” Alea. Instituto
Nacional de Matematica Pura e Aplicada, 2024. https://doi.org/10.30757/ALEA.V21-70.
ieee: K. S. CZUDEK and D. Dolgopyat, “The central limit theorem and rate of mixing
for simple random walks on the circle,” Alea, vol. 21, no. 2. Instituto
Nacional de Matematica Pura e Aplicada, pp. 1853–1865, 2024.
ista: CZUDEK KS, Dolgopyat D. 2024. The central limit theorem and rate of mixing
for simple random walks on the circle. Alea. 21(2), 1853–1865.
mla: CZUDEK, Klaudiusz S., and Dmitry Dolgopyat. “The Central Limit Theorem and
Rate of Mixing for Simple Random Walks on the Circle.” Alea, vol. 21, no.
2, Instituto Nacional de Matematica Pura e Aplicada, 2024, pp. 1853–65, doi:10.30757/ALEA.V21-70.
short: K.S. CZUDEK, D. Dolgopyat, Alea 21 (2024) 1853–1865.
date_created: 2024-11-24T23:01:49Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-08T14:48:42Z
day: '01'
department:
- _id: VaKa
doi: 10.30757/ALEA.V21-70
ec_funded: 1
external_id:
arxiv:
- '2404.11700'
isi:
- '001440992000003'
fulldoi: https://doi.org/10.30757/ALEA.V21-70
intvolume: ' 21'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: ' https://doi.org/10.48550/arXiv.2404.11700'
month: '11'
oa: 1
oa_version: Preprint
page: 1853-1865
project:
- _id: fc2ed2f7-9c52-11eb-aca3-c01059dda49c
call_identifier: H2020
grant_number: '101034413'
name: 'IST-BRIDGE: International postdoctoral program'
publication: Alea
publication_identifier:
issn:
- 1980-0436
publication_status: published
publisher: Instituto Nacional de Matematica Pura e Aplicada
quality_controlled: '1'
scopus_import: '1'
status: public
title: The central limit theorem and rate of mixing for simple random walks on the
circle
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 21
year: '2024'
...
---
_id: '17475'
abstract:
- lang: eng
text: "As a discrete analogue of Kac’s celebrated question on ‘hearing the shape
of a drum’ and towards a practical\r\ngraph isomorphism test, it is of interest
to understand which graphs are determined up to isomorphism by\r\ntheir spectrum
(of their adjacency matrix). A striking conjecture in this area, due to van Dam
and Haemers,\r\nis that ‘almost all graphs are determined by their spectrum’,
meaning that the fraction of unlabelled n-vertex\r\ngraphs which are determined
by their spectrum converges to 1 as n → ∞.\r\nIn this paper, we make a step towards
this conjecture, showing that there are exponentially many n-vertex\r\ngraphs
which are determined by their spectrum. This improves on previous bounds (of shape
e\r\nc\r\n√\r\nn\r\n). We also\r\npropose a number of further directions of research.\r\n"
acknowledgement: Matthew Kwan was supported by ERC Starting Grant ‘RANDSTRUCT’ No.
101076777.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Illya
full_name: Koval, Illya
id: 2eed1f3b-896a-11ed-bdf8-93c7c4bf159e
last_name: Koval
- first_name: Matthew Alan
full_name: Kwan, Matthew Alan
id: 5fca0887-a1db-11eb-95d1-ca9d5e0453b3
last_name: Kwan
orcid: 0000-0002-4003-7567
citation:
ama: Koval I, Kwan MA. Exponentially many graphs are determined by their spectrum.
Quarterly Journal of Mathematics. 2024;75(3):869-899. doi:10.1093/qmath/haae030
apa: Koval, I., & Kwan, M. A. (2024). Exponentially many graphs are determined
by their spectrum. Quarterly Journal of Mathematics. Oxford University
Press. https://doi.org/10.1093/qmath/haae030
chicago: Koval, Illya, and Matthew Alan Kwan. “Exponentially Many Graphs Are Determined
by Their Spectrum.” Quarterly Journal of Mathematics. Oxford University
Press, 2024. https://doi.org/10.1093/qmath/haae030.
ieee: I. Koval and M. A. Kwan, “Exponentially many graphs are determined by their
spectrum,” Quarterly Journal of Mathematics, vol. 75, no. 3. Oxford University
Press, pp. 869–899, 2024.
ista: Koval I, Kwan MA. 2024. Exponentially many graphs are determined by their
spectrum. Quarterly Journal of Mathematics. 75(3), 869–899.
mla: Koval, Illya, and Matthew Alan Kwan. “Exponentially Many Graphs Are Determined
by Their Spectrum.” Quarterly Journal of Mathematics, vol. 75, no. 3, Oxford
University Press, 2024, pp. 869–99, doi:10.1093/qmath/haae030.
short: I. Koval, M.A. Kwan, Quarterly Journal of Mathematics 75 (2024) 869–899.
corr_author: '1'
date_created: 2024-09-01T22:01:07Z
date_published: 2024-06-19T00:00:00Z
date_updated: 2025-09-08T09:09:41Z
day: '19'
ddc:
- '500'
department:
- _id: MaKw
- _id: VaKa
doi: 10.1093/qmath/haae030
external_id:
arxiv:
- '2309.09788'
isi:
- '001249741500001'
file:
- access_level: open_access
checksum: abf200d37ad69e6f2c0750a30296ad97
content_type: application/pdf
creator: cchlebak
date_created: 2024-09-06T12:23:57Z
date_updated: 2024-09-06T12:23:57Z
file_id: '17851'
file_name: 2024_QuJofMath_Koval.pdf
file_size: 946411
relation: main_file
success: 1
file_date_updated: 2024-09-06T12:23:57Z
fulldoi: https://doi.org/10.1093/qmath/haae030
has_accepted_license: '1'
intvolume: ' 75'
isi: 1
issue: '3'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 869-899
project:
- _id: bd95085b-d553-11ed-ba76-e55d3349be45
grant_number: '101076777'
name: Randomness and structure in combinatorics
publication: Quarterly Journal of Mathematics
publication_identifier:
eissn:
- 1464-3847
issn:
- 0033-5606
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Exponentially many graphs are determined by their spectrum
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 75
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '18065'
abstract:
- lang: eng
text: We establish a close connection between acceleration and dynamical degree
for one-frequency quasi-periodic compact cocycles, by showing that two vectors
derived separately from each coincide. Based on this, we provide a dynamical classification
of one-frequency quasi-periodic SO(3, R)-cocycles.
acknowledgement: "X. Hou is partially supported by National Natural Science Foundation
of China (Grant \r\n12071083) and Funds for Distinguished Youths of Hubei Province
of China (\r\n2019CFA680). Y. Pan is supported by ERC Advanced Grant (#885707).
Q. Zhou is partially supported by National Key R&D Program of China (2020YFA0713300),
NSFC grant (\r\n12071232) and Nankai Zhide Foundation."
article_number: '109943'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Xuanji
full_name: Hou, Xuanji
last_name: Hou
- first_name: Yi
full_name: Pan, Yi
id: 1e21c7f7-9070-11eb-847d-8b04c7169523
last_name: Pan
- first_name: Qi
full_name: Zhou, Qi
last_name: Zhou
citation:
ama: Hou X, Pan Y, Zhou Q. Dynamical classification of analytic one-frequency quasi-periodic
SO(3,R)-cocycles. Advances in Mathematics. 2024;457. doi:10.1016/j.aim.2024.109943
apa: Hou, X., Pan, Y., & Zhou, Q. (2024). Dynamical classification of analytic
one-frequency quasi-periodic SO(3,R)-cocycles. Advances in Mathematics.
Elsevier. https://doi.org/10.1016/j.aim.2024.109943
chicago: Hou, Xuanji, Yi Pan, and Qi Zhou. “Dynamical Classification of Analytic
One-Frequency Quasi-Periodic SO(3,R)-Cocycles.” Advances in Mathematics.
Elsevier, 2024. https://doi.org/10.1016/j.aim.2024.109943.
ieee: X. Hou, Y. Pan, and Q. Zhou, “Dynamical classification of analytic one-frequency
quasi-periodic SO(3,R)-cocycles,” Advances in Mathematics, vol. 457. Elsevier,
2024.
ista: Hou X, Pan Y, Zhou Q. 2024. Dynamical classification of analytic one-frequency
quasi-periodic SO(3,R)-cocycles. Advances in Mathematics. 457, 109943.
mla: Hou, Xuanji, et al. “Dynamical Classification of Analytic One-Frequency Quasi-Periodic
SO(3,R)-Cocycles.” Advances in Mathematics, vol. 457, 109943, Elsevier,
2024, doi:10.1016/j.aim.2024.109943.
short: X. Hou, Y. Pan, Q. Zhou, Advances in Mathematics 457 (2024).
corr_author: '1'
date_created: 2024-09-15T22:01:39Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2025-09-08T09:44:19Z
day: '01'
ddc:
- '510'
department:
- _id: VaKa
doi: 10.1016/j.aim.2024.109943
ec_funded: 1
external_id:
arxiv:
- '2311.17537'
isi:
- '001315306500001'
file:
- access_level: open_access
checksum: 1c80b844a91d93cf4799f4a65873b18d
content_type: application/pdf
creator: dernst
date_created: 2025-01-13T08:29:27Z
date_updated: 2025-01-13T08:29:27Z
file_id: '18826'
file_name: 2024_AdvancesMath_Hou.pdf
file_size: 713659
relation: main_file
success: 1
file_date_updated: 2025-01-13T08:29:27Z
fulldoi: https://doi.org/10.1016/j.aim.2024.109943
has_accepted_license: '1'
intvolume: ' 457'
isi: 1
language:
- iso: eng
month: '11'
oa: 1
oa_version: Published Version
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Advances in Mathematics
publication_identifier:
eissn:
- 1090-2082
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dynamical classification of analytic one-frequency quasi-periodic SO(3,R)-cocycles
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: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 457
year: '2024'
...
---
OA_type: free access
_id: '17231'
abstract:
- lang: eng
text: In the class of projective billiards, which contains the usual billiards,
we exhibit counter-examples to Ivrii's conjecture, which states that in any planar
billiard with smooth boundary the set of periodic orbits has zero measure. The
counter-examples are polygons admitting a 2-parameters family of n-periodic orbits,
with n being either 3 or any even integer greater than 4.
article_processing_charge: No
article_type: original
author:
- first_name: Corentin
full_name: Fiorebe, Corentin
id: 06619f18-9070-11eb-847d-d1ee780bd88b
last_name: Fiorebe
citation:
ama: Fiorebe C. Examples of projective billiards with open sets of periodic orbits.
Discrete and Continuous Dynamical Systems- Series A. 2024;44(11):3287-3301.
doi:10.3934/dcds.2024059
apa: Fiorebe, C. (2024). Examples of projective billiards with open sets of periodic
orbits. Discrete and Continuous Dynamical Systems- Series A. AIMS. https://doi.org/10.3934/dcds.2024059
chicago: Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of
Periodic Orbits.” Discrete and Continuous Dynamical Systems- Series A.
AIMS, 2024. https://doi.org/10.3934/dcds.2024059.
ieee: C. Fiorebe, “Examples of projective billiards with open sets of periodic orbits,”
Discrete and Continuous Dynamical Systems- Series A, vol. 44, no. 11. AIMS,
pp. 3287–3301, 2024.
ista: Fiorebe C. 2024. Examples of projective billiards with open sets of periodic
orbits. Discrete and Continuous Dynamical Systems- Series A. 44(11), 3287–3301.
mla: Fiorebe, Corentin. “Examples of Projective Billiards with Open Sets of Periodic
Orbits.” Discrete and Continuous Dynamical Systems- Series A, vol. 44,
no. 11, AIMS, 2024, pp. 3287–301, doi:10.3934/dcds.2024059.
short: C. Fiorebe, Discrete and Continuous Dynamical Systems- Series A 44 (2024)
3287–3301.
corr_author: '1'
date_created: 2024-07-14T22:01:10Z
date_published: 2024-11-01T00:00:00Z
date_updated: 2026-08-12T06:19:26Z
day: '01'
ddc:
- '500'
department:
- _id: VaKa
doi: 10.3934/dcds.2024059
external_id:
isi:
- '001230091000001'
fulldoi: https://doi.org/10.3934/dcds.2024059
intvolume: ' 44'
isi: 1
issue: '11'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.3934/dcds.2024059
month: '11'
oa: 1
oa_version: Published Version
page: 3287-3301
publication: Discrete and Continuous Dynamical Systems- Series A
publication_identifier:
eissn:
- 1553-5231
issn:
- 1078-0947
publication_status: published
publisher: AIMS
quality_controlled: '1'
scopus_import: '1'
status: public
title: Examples of projective billiards with open sets of periodic orbits
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 44
year: '2024'
...
---
_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: 2025-04-14T07:53:46Z
day: '01'
department:
- _id: VaKa
doi: 10.1007/s00222-023-01191-8
ec_funded: 1
external_id:
arxiv:
- '1905.00890'
isi:
- '000978887600001'
fulldoi: https://doi.org/10.1007/s00222-023-01191-8
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: '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;404:1-50.
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,
vol. 404. Springer Nature, pp. 1–50, 2023.
ista: Chen J, Kaloshin V, Zhang HK. 2023. Length spectrum rigidity for piecewise
analytic Bunimovich billiards. Communications in Mathematical Physics. 404, 1–50.
mla: Chen, Jianyu, et al. “Length Spectrum Rigidity for Piecewise Analytic Bunimovich
Billiards.” Communications in Mathematical Physics, vol. 404, Springer
Nature, 2023, pp. 1–50, doi:10.1007/s00220-023-04837-z.
short: J. Chen, V. Kaloshin, H.K. Zhang, Communications in Mathematical Physics
404 (2023) 1–50.
corr_author: '1'
date_created: 2023-10-15T22:01:11Z
date_published: 2023-11-01T00:00:00Z
date_updated: 2025-04-14T07:53:45Z
day: '01'
department:
- _id: VaKa
doi: 10.1007/s00220-023-04837-z
ec_funded: 1
external_id:
arxiv:
- '1902.07330'
isi:
- '001073177200001'
fulldoi: https://doi.org/10.1007/s00220-023-04837-z
intvolume: ' 404'
isi: 1
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1902.07330
month: '11'
oa: 1
oa_version: Preprint
page: 1-50
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: published
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
volume: 404
year: '2023'
...
---
_id: '18959'
abstract:
- lang: eng
text: This workshop continues a series of workshops whose current format originated
in 1981 under then-organizers Moser and Zehnder, and whose latest iteration took
place in July 2023. The general goal of this series of workshops is to discuss
the latest developments in the field of dynamical systems, broadly construed,
and its connections with neighboring areas of mathematics such as differential
geometry, partial differential equations, and more recently contact and symplectic
geometry. We continued this tradition, bringing in new participants working in
areas of dynamical systems and its connections with other areas of mathematics
that are currently highly active and/or showing great promise for future development.
Key focus areas for the 2023 workshop include spectral rigidity for planar domains,
chaotic and oscillatory motions in celestial mechanics, conformal symplectic dynamics,
and relations between dynamics.he workshop by the grant DMS-2230648, “US Junior
Oberwolfach Fellows”.
acknowledgement: The MFO and the workshop organizers would like to thank the National
Science Foundation for supporting the participation of junior researchers in the
workshop by the grant DMS-2230648, “US Junior Oberwolfach Fellows”.
article_processing_charge: No
article_type: original
author:
- first_name: Marie-Claude
full_name: Arnaud, Marie-Claude
last_name: Arnaud
- first_name: Michael
full_name: Hutchings, Michael
last_name: Hutchings
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Arnaud M-C, Hutchings M, Kaloshin V. Dynamische Systeme. Oberwolfach Reports.
2023;20(3):1671-1730. doi:10.4171/owr/2023/30
apa: Arnaud, M.-C., Hutchings, M., & Kaloshin, V. (2023). Dynamische Systeme.
Oberwolfach Reports. EMS Press. https://doi.org/10.4171/owr/2023/30
chicago: Arnaud, Marie-Claude, Michael Hutchings, and Vadim Kaloshin. “Dynamische
Systeme.” Oberwolfach Reports. EMS Press, 2023. https://doi.org/10.4171/owr/2023/30.
ieee: M.-C. Arnaud, M. Hutchings, and V. Kaloshin, “Dynamische Systeme,” Oberwolfach
Reports, vol. 20, no. 3. EMS Press, pp. 1671–1730, 2023.
ista: Arnaud M-C, Hutchings M, Kaloshin V. 2023. Dynamische Systeme. Oberwolfach
Reports. 20(3), 1671–1730.
mla: Arnaud, Marie-Claude, et al. “Dynamische Systeme.” Oberwolfach Reports,
vol. 20, no. 3, EMS Press, 2023, pp. 1671–730, doi:10.4171/owr/2023/30.
short: M.-C. Arnaud, M. Hutchings, V. Kaloshin, Oberwolfach Reports 20 (2023) 1671–1730.
date_created: 2025-01-29T13:19:15Z
date_published: 2023-07-09T00:00:00Z
date_updated: 2025-01-29T13:23:15Z
day: '09'
department:
- _id: VaKa
doi: 10.4171/owr/2023/30
fulldoi: https://doi.org/10.4171/owr/2023/30
intvolume: ' 20'
issue: '3'
language:
- iso: eng
month: '07'
oa_version: None
page: 1671-1730
publication: Oberwolfach Reports
publication_identifier:
eissn:
- 1660-8941
issn:
- 1660-8933
publication_status: published
publisher: EMS Press
quality_controlled: '1'
status: public
title: Dynamische Systeme
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 20
year: '2023'
...
---
OA_place: publisher
OA_type: hybrid
_id: '11553'
abstract:
- lang: eng
text: "In holomorphic dynamics, complex box mappings arise as first return maps
to wellchosen domains. They are a generalization of polynomial-like mapping, where
the domain of the return map can have infinitely many components. They turned
out to be extremely useful in tackling diverse problems. The purpose of this paper
is:\r\n• To illustrate some pathologies that can occur when a complex box mapping
is not induced by a globally defined map and when its domain has infinitely many
components, and to give conditions to avoid these issues.\r\n• To show that once
one has a box mapping for a rational map, these conditions can be assumed to hold
in a very natural setting. Thus, we call such complex box mappings dynamically
natural. Having such box mappings is the first step in tackling many problems
in one-dimensional dynamics.\r\n• Many results in holomorphic dynamics rely on
an interplay between combinatorial and analytic techniques. In this setting, some
of these tools are:\r\n • the Enhanced Nest (a nest of puzzle pieces around critical
points) from Kozlovski, Shen, van Strien (AnnMath 165:749–841, 2007), referred
to below as KSS;\r\n • the Covering Lemma (which controls the moduli of pullbacks
of annuli) from Kahn and Lyubich (Ann Math 169(2):561–593, 2009);\r\n • the
QC-Criterion and the Spreading Principle from KSS.\r\nThe purpose of this paper
is to make these tools more accessible so that they can be used as a ‘black box’,
so one does not have to redo the proofs in new settings.\r\n• To give an intuitive,
but also rather detailed, outline of the proof from KSS and Kozlovski and van
Strien (Proc Lond Math Soc (3) 99:275–296, 2009) of the following results for
non-renormalizable dynamically natural complex box mappings:\r\n • puzzle pieces
shrink to points,\r\n • (under some assumptions) topologically conjugate non-renormalizable
polynomials and box mappings are quasiconformally conjugate.\r\n• We prove the
fundamental ergodic properties for dynamically natural box mappings. This leads
to some necessary conditions for when such a box mapping supports a measurable
invariant line field on its filled Julia set. These mappings\r\nare the analogues
of Lattès maps in this setting.\r\n• We prove a version of Mañé’s Theorem for
complex box mappings concerning expansion along orbits of points that avoid a
neighborhood of the set of critical points."
acknowledgement: We would also like to thank Dzmitry Dudko and Dierk Schleicher for
many stimulating discussions and encouragement during our work on this project,
and Weixiao Shen, Mikhail Hlushchanka and the referee for helpful comments. We are
grateful to Leon Staresinic who carefully read the revised version of the manuscript
and provided many helpful suggestions.
article_processing_charge: No
article_type: original
author:
- first_name: Trevor
full_name: Clark, Trevor
last_name: Clark
- first_name: Kostiantyn
full_name: Drach, Kostiantyn
id: fe8209e2-906f-11eb-847d-950f8fc09115
last_name: Drach
orcid: 0000-0002-9156-8616
- first_name: Oleg
full_name: Kozlovski, Oleg
last_name: Kozlovski
- first_name: Sebastian Van
full_name: Strien, Sebastian Van
last_name: Strien
citation:
ama: Clark T, Drach K, Kozlovski O, Strien SV. The dynamics of complex box mappings.
Arnold Mathematical Journal. 2022;8(2):319-410. doi:10.1007/s40598-022-00200-7
apa: Clark, T., Drach, K., Kozlovski, O., & Strien, S. V. (2022). The dynamics
of complex box mappings. Arnold Mathematical Journal. Springer Nature.
https://doi.org/10.1007/s40598-022-00200-7
chicago: Clark, Trevor, Kostiantyn Drach, Oleg Kozlovski, and Sebastian Van Strien.
“The Dynamics of Complex Box Mappings.” Arnold Mathematical Journal. Springer
Nature, 2022. https://doi.org/10.1007/s40598-022-00200-7.
ieee: T. Clark, K. Drach, O. Kozlovski, and S. V. Strien, “The dynamics of complex
box mappings,” Arnold Mathematical Journal, vol. 8, no. 2. Springer Nature,
pp. 319–410, 2022.
ista: Clark T, Drach K, Kozlovski O, Strien SV. 2022. The dynamics of complex box
mappings. Arnold Mathematical Journal. 8(2), 319–410.
mla: Clark, Trevor, et al. “The Dynamics of Complex Box Mappings.” Arnold Mathematical
Journal, vol. 8, no. 2, Springer Nature, 2022, pp. 319–410, doi:10.1007/s40598-022-00200-7.
short: T. Clark, K. Drach, O. Kozlovski, S.V. Strien, Arnold Mathematical Journal
8 (2022) 319–410.
date_created: 2022-07-10T22:01:53Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2025-07-10T11:50:12Z
day: '01'
ddc:
- '500'
department:
- _id: VaKa
doi: 10.1007/s40598-022-00200-7
ec_funded: 1
file:
- access_level: open_access
checksum: 16e7c659dee9073c6c8aeb87316ef201
content_type: application/pdf
creator: kschuh
date_created: 2022-07-12T10:04:55Z
date_updated: 2022-07-12T10:04:55Z
file_id: '11559'
file_name: 2022_ArnoldMathematicalJournal_Clark.pdf
file_size: 2509915
relation: main_file
success: 1
file_date_updated: 2022-07-12T10:04:55Z
fulldoi: https://doi.org/10.1007/s40598-022-00200-7
has_accepted_license: '1'
intvolume: ' 8'
issue: '2'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
page: 319-410
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Arnold Mathematical Journal
publication_identifier:
eissn:
- 2199-6806
issn:
- 2199-6792
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- relation: erratum
url: https://doi.org/10.1007/s40598-022-00209-y
- relation: erratum
url: https://doi.org/10.1007/s40598-022-00218-x
scopus_import: '1'
status: public
title: The dynamics of complex box mappings
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2022'
...
---
_id: '11717'
abstract:
- lang: eng
text: "We study rigidity of rational maps that come from Newton's root finding method
for polynomials of arbitrary degrees. We establish dynamical rigidity of these
maps: each point in the Julia set of a Newton map is either rigid (i.e. its orbit
can be distinguished in combinatorial terms from all other orbits), or the orbit
of this point eventually lands in the filled-in Julia set of a polynomial-like
restriction of the original map. As a corollary, we show that the Julia sets of
Newton maps in many non-trivial cases are locally connected; in particular, every
cubic Newton map without Siegel points has locally connected Julia set.\r\nIn
the parameter space of Newton maps of arbitrary degree we obtain the following
rigidity result: any two combinatorially equivalent Newton maps are quasiconformally
conjugate in a neighborhood of their Julia sets provided that they either non-renormalizable,
or they are both renormalizable “in the same way”.\r\nOur main tool is a generalized
renormalization concept called “complex box mappings” for which we extend a dynamical
rigidity result by Kozlovski and van Strien so as to include irrationally indifferent
and renormalizable situations."
acknowledgement: 'We are grateful to a number of colleagues for helpful and inspiring
discussions during the time when we worked on this project, in particular Dima Dudko,
Misha Hlushchanka, John Hubbard, Misha Lyubich, Oleg Kozlovski, and Sebastian van
Strien. Finally, we would like to thank our dynamics research group for numerous
helpful and enjoyable discussions: Konstantin Bogdanov, Roman Chernov, Russell Lodge,
Steffen Maaß, David Pfrang, Bernhard Reinke, Sergey Shemyakov, and Maik Sowinski.
We gratefully acknowledge support by the Advanced Grant “HOLOGRAM” (#695 621) of
the European Research Council (ERC), as well as hospitality of Cornell University
in the spring of 2018 while much of this work was prepared. The first-named author
also acknowledges the support of the ERC Advanced Grant “SPERIG” (#885 707).'
article_number: '108591'
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Kostiantyn
full_name: Drach, Kostiantyn
id: fe8209e2-906f-11eb-847d-950f8fc09115
last_name: Drach
orcid: 0000-0002-9156-8616
- first_name: Dierk
full_name: Schleicher, Dierk
last_name: Schleicher
citation:
ama: Drach K, Schleicher D. Rigidity of Newton dynamics. Advances in Mathematics.
2022;408(Part A). doi:10.1016/j.aim.2022.108591
apa: Drach, K., & Schleicher, D. (2022). Rigidity of Newton dynamics. Advances
in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2022.108591
chicago: Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.”
Advances in Mathematics. Elsevier, 2022. https://doi.org/10.1016/j.aim.2022.108591.
ieee: K. Drach and D. Schleicher, “Rigidity of Newton dynamics,” Advances in
Mathematics, vol. 408, no. Part A. Elsevier, 2022.
ista: Drach K, Schleicher D. 2022. Rigidity of Newton dynamics. Advances in Mathematics.
408(Part A), 108591.
mla: Drach, Kostiantyn, and Dierk Schleicher. “Rigidity of Newton Dynamics.” Advances
in Mathematics, vol. 408, no. Part A, 108591, Elsevier, 2022, doi:10.1016/j.aim.2022.108591.
short: K. Drach, D. Schleicher, Advances in Mathematics 408 (2022).
corr_author: '1'
date_created: 2022-08-01T17:08:16Z
date_published: 2022-10-29T00:00:00Z
date_updated: 2025-04-14T07:53:45Z
day: '29'
ddc:
- '510'
department:
- _id: VaKa
doi: 10.1016/j.aim.2022.108591
ec_funded: 1
external_id:
isi:
- '000860924200005'
file:
- access_level: open_access
checksum: 2710e6f5820f8c20a676ddcbb30f0e8d
content_type: application/pdf
creator: dernst
date_created: 2023-02-02T07:39:09Z
date_updated: 2023-02-02T07:39:09Z
file_id: '12474'
file_name: 2022_AdvancesMathematics_Drach.pdf
file_size: 2164036
relation: main_file
success: 1
file_date_updated: 2023-02-02T07:39:09Z
fulldoi: https://doi.org/10.1016/j.aim.2022.108591
has_accepted_license: '1'
intvolume: ' 408'
isi: 1
issue: Part A
keyword:
- General Mathematics
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
project:
- _id: 9B8B92DE-BA93-11EA-9121-9846C619BF3A
call_identifier: H2020
grant_number: '885707'
name: Spectral rigidity and integrability for billiards and geodesic flows
publication: Advances in Mathematics
publication_identifier:
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Rigidity of Newton dynamics
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: 408
year: '2022'
...
---
_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.
corr_author: '1'
date_created: 2023-01-12T12:06:49Z
date_published: 2022-10-03T00:00:00Z
date_updated: 2025-04-14T07:53:45Z
day: '03'
department:
- _id: VaKa
doi: 10.1134/S1560354722050021
ec_funded: 1
external_id:
arxiv:
- '2105.14640'
isi:
- '000865267300002'
fulldoi: https://doi.org/10.1134/S1560354722050021
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: '10706'
abstract:
- lang: eng
text: This is a collection of problems composed by some participants of the workshop
“Differential Geometry, Billiards, and Geometric Optics” that took place at CIRM
on October 4–8, 2021.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Misha
full_name: Bialy, Misha
last_name: Bialy
- first_name: Corentin
full_name: Fiorebe, Corentin
id: 06619f18-9070-11eb-847d-d1ee780bd88b
last_name: Fiorebe
- first_name: Alexey
full_name: Glutsyuk, Alexey
last_name: Glutsyuk
- first_name: Mark
full_name: Levi, Mark
last_name: Levi
- first_name: Alexander
full_name: Plakhov, Alexander
last_name: Plakhov
- first_name: Serge
full_name: Tabachnikov, Serge
last_name: Tabachnikov
citation:
ama: Bialy M, Fiorebe C, Glutsyuk A, Levi M, Plakhov A, Tabachnikov S. Open problems
on billiards and geometric optics. Arnold Mathematical Journal. 2022;8:411-422.
doi:10.1007/s40598-022-00198-y
apa: 'Bialy, M., Fiorebe, C., Glutsyuk, A., Levi, M., Plakhov, A., & Tabachnikov,
S. (2022). Open problems on billiards and geometric optics. Arnold Mathematical
Journal. Hybrid: Springer Nature. https://doi.org/10.1007/s40598-022-00198-y'
chicago: Bialy, Misha, Corentin Fiorebe, Alexey Glutsyuk, Mark Levi, Alexander Plakhov,
and Serge Tabachnikov. “Open Problems on Billiards and Geometric Optics.” Arnold
Mathematical Journal. Springer Nature, 2022. https://doi.org/10.1007/s40598-022-00198-y.
ieee: M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, and S. Tabachnikov,
“Open problems on billiards and geometric optics,” Arnold Mathematical Journal,
vol. 8. Springer Nature, pp. 411–422, 2022.
ista: Bialy M, Fiorebe C, Glutsyuk A, Levi M, Plakhov A, Tabachnikov S. 2022. Open
problems on billiards and geometric optics. Arnold Mathematical Journal. 8, 411–422.
mla: Bialy, Misha, et al. “Open Problems on Billiards and Geometric Optics.” Arnold
Mathematical Journal, vol. 8, Springer Nature, 2022, pp. 411–22, doi:10.1007/s40598-022-00198-y.
short: M. Bialy, C. Fiorebe, A. Glutsyuk, M. Levi, A. Plakhov, S. Tabachnikov, Arnold
Mathematical Journal 8 (2022) 411–422.
conference:
end_date: 2021-10-08
location: Hybrid
name: 'CIRM: Centre International de Rencontres Mathématiques'
start_date: 2021-10-04
date_created: 2022-01-30T23:01:34Z
date_published: 2022-10-01T00:00:00Z
date_updated: 2023-02-27T07:34:08Z
day: '01'
department:
- _id: VaKa
doi: 10.1007/s40598-022-00198-y
external_id:
arxiv:
- '2110.10750'
fulldoi: https://doi.org/10.1007/s40598-022-00198-y
intvolume: ' 8'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2110.10750
month: '10'
oa: 1
oa_version: Preprint
page: 411-422
publication: Arnold Mathematical Journal
publication_identifier:
eissn:
- 2199-6806
issn:
- 2199-6792
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
related_material:
link:
- relation: earlier_version
url: https://conferences.cirm-math.fr/2383.html
scopus_import: '1'
status: public
title: Open problems on billiards and geometric optics
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 8
year: '2022'
...
---
_id: '17063'
abstract:
- lang: eng
text: This workshop continued a biannual series of workshops at Oberwolfach on dynamical
systems that started with a meeting organized by Moser and Zehnder in 1981. Workshops
in this series focus on new results and developments in dynamical systems and
related areas of mathematics, with symplectic geometry playing an important role
in recent years in connection with Hamiltonian dynamics. In this year special
emphasis was placed on various kinds of spectra (in contact geometry, in Riemannian
geometry, in dynamical systems and in symplectic topology) and their applications
to dynamics.
article_processing_charge: No
article_type: original
author:
- first_name: Marie-Claude
full_name: Arnaud, Marie-Claude
last_name: Arnaud
- first_name: Helmut W.
full_name: Hofer, Helmut W.
last_name: Hofer
- first_name: Michael
full_name: Hutchings, Michael
last_name: Hutchings
- first_name: Vadim
full_name: Kaloshin, Vadim
id: FE553552-CDE8-11E9-B324-C0EBE5697425
last_name: Kaloshin
orcid: 0000-0002-6051-2628
citation:
ama: Arnaud M-C, Hofer HW, Hutchings M, Kaloshin V. Dynamische Systeme. Oberwolfach
Reports. 2022;18(3):1735-1803. doi:10.4171/owr/2021/33
apa: Arnaud, M.-C., Hofer, H. W., Hutchings, M., & Kaloshin, V. (2022). Dynamische
Systeme. Oberwolfach Reports. EMS Press. https://doi.org/10.4171/owr/2021/33
chicago: Arnaud, Marie-Claude, Helmut W. Hofer, Michael Hutchings, and Vadim Kaloshin.
“Dynamische Systeme.” Oberwolfach Reports. EMS Press, 2022. https://doi.org/10.4171/owr/2021/33.
ieee: M.-C. Arnaud, H. W. Hofer, M. Hutchings, and V. Kaloshin, “Dynamische Systeme,”
Oberwolfach Reports, vol. 18, no. 3. EMS Press, pp. 1735–1803, 2022.
ista: Arnaud M-C, Hofer HW, Hutchings M, Kaloshin V. 2022. Dynamische Systeme. Oberwolfach
Reports. 18(3), 1735–1803.
mla: Arnaud, Marie-Claude, et al. “Dynamische Systeme.” Oberwolfach Reports,
vol. 18, no. 3, EMS Press, 2022, pp. 1735–803, doi:10.4171/owr/2021/33.
short: M.-C. Arnaud, H.W. Hofer, M. Hutchings, V. Kaloshin, Oberwolfach Reports
18 (2022) 1735–1803.
corr_author: '1'
das_tickbox: '1'
date_created: 2024-05-29T06:01:19Z
date_published: 2022-11-26T00:00:00Z
date_updated: 2026-07-06T11:52:32Z
day: '26'
ddc:
- '500'
department:
- _id: VaKa
doi: 10.4171/owr/2021/33
fulldoi: https://doi.org/10.4171/owr/2021/33
intvolume: ' 18'
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://www.doi.org/10.4171/OWR/2021/33
month: '11'
oa: 1
oa_version: Published Version
page: 1735-1803
publication: Oberwolfach Reports
publication_identifier:
eissn:
- 1660-8941
issn:
- 1660-8933
publication_status: published
publisher: EMS Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: Dynamische Systeme
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 18
year: '2022'
...