Spectral rigidity and integrability for billiards and geodesic flows

Project Information

SPERIG

Grant agreement ID: 885707

DOI

10.3030/885707

Project closed

EC signature date 19 May 2020

Start date 1 March 2021

End date 28 February 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 820 816,00

EU contribution

€ 1 820 816,00

Coordinated by

INSTITUTE OF SCIENCE AND TECHNOLOGY AUSTRIA
Austria

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Other (14)

Unmarked spectral rigidity of expanding circle maps

Author(s): Kostiantyn Drach, Vadim Kaloshin
Published in: 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2511.17452

Rigidity of the Suris' potential in the Frenkel-Kontorova Model

Author(s): Corentin Fierobe, Daniel Tsodikovich
Published in: 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2601.15058

Computation of a separatrix map and a normally hyperbolic invariant lamination for the RP3BP

Author(s): Marcel Guardia, Vadim Kaloshin, Pau Martín, Pablo Roldan
Published in: 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2603.19893

MARKED LENGTH SPECTRAL DETERMINATION OF ANALYTIC CHAOTIC BILLIARDS WITH AXIAL SYMMETRIES

Author(s): JACOPO DE SIMOI, VADIM KALOSHIN, MARTIN LEGUIL
Published in: 2022
Publisher: arXiv
DOI: 10.48550/arxiv.1905.00890

Normal distribution of Lyapunov exponents of periodic orbits for expanding circle maps

Author(s): Kostiantyn Drach, Zhi Fu, Vadim Kaloshin, Zhiqiang Li, Carlangelo Liverani
Published in: 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2511.15662

Spectral rigidity of Liouville tori

Author(s): Joscha Henheik, Vadim Kaloshin, Yunzhe Li, Amir Vig
Published in: 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2511.10398

Stochastic behavior along mean motion resonances in the restricted planar 3-body problem

Author(s): Marcel Guardia, Vadim Kaloshin, Pau Martín, Pablo Roldan
Published in: 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2603.19894

Billiard tables with analytic Birkhoff normal form are generically Gevrey divergent

Author(s): Illya Koval
Published in: 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2403.14448

Exponentially many graphs are determined by their spectrum

Author(s): Illya Koval, Matthew Kwan
Published in: 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2309.09788

Balian-Bloch Wave Invariants for Nearly Degenerate Orbits

Author(s): Kaloshin, Vadim; Koval, Illya; Vig, Amir
Published in: Issue 3, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2404.02381

Deformations of the Standard Map with Prescribed Actions and Lyapunov Exponents

Author(s): Yunzhe Li
Published in: 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2512.03865

Kuznecov remainders and generic metrics

Author(s): Vadim Kaloshin, Emmett L. Wyman, Yakun Xi
Published in: 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2507.06887

A billiard table close to an ellipse is deformationally spectrally rigid among dihedrally symmetric domains

Author(s): Corentin Fierobe, Vadim Kaloshin, Alfonso Sorrentino
Published in: 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2511.20062

Silent Orbits and Cancellations in the Wave Trace

Author(s): Illya Koval, Amir Vig
Published in: 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2408.09238

Peer reviewed articles (10)

Local Rigidity for Symplectic Billiards

Author(s): Daniel Tsodikovich
Published in: The Journal of Geometric Analysis, Issue 35, 2025, ISSN 1050-6926
Publisher: American Mathematical Society
DOI: 10.1007/s12220-025-02148-4

Addendum to “A Hyperbolic View of the Seven Circles Theorem”

Author(s): Kostiantyn Drach, Richard Evan Schwartz
Published in: The Mathematical Intelligencer, Issue 45, 2023, Page(s) 91-91, ISSN 0343-6993
Publisher: Springer Verlag
DOI: 10.1007/s00283-022-10231-9

Partial Frequency and Frequency Ratio in Multiscale KAM Formulism

Author(s): Weichao Qian, Xue Yang, Yong Li
Published in: Journal of Dynamics and Differential Equations, 2025, ISSN 1040-7294
Publisher: Plenum Publishers
DOI: 10.1007/s10884-025-10422-w

Local strong Birkhoff conjecture and local spectral uniqueness of almost every ellipse

Author(s): Illya Koval
Published in: Inventiones mathematicae, Issue 244, 2026, Page(s) 221-298, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-025-01397-y

Every diffeomorphism is a total renormalization of a close to identity map

Author(s): Pierre Berger, Nicolaz Gourmelon, Mathieu Helfter
Published in: Inventiones mathematicae, Issue 239, 2025, Page(s) 431-468, ISSN 0020-9910
Publisher: Springer Verlag
DOI: 10.1007/s00222-024-01305-w

Length Spectrum Rigidity for Piecewise Analytic Bunimovich Billiards

Author(s): Jianyu Chen; Vadim Kaloshin; Hong-Kun Zhang
Published in: Communications in Mathematical Physics, 2023, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-023-04837-z

Erratum to: On Some Invariants of Birkhoff Billiards Under Conjugacy

Author(s): Comlan E. Koudjinan, Vadim Kaloshin
Published in: Regular and Chaotic Dynamics, Issue 27, 2023, Page(s) 757-757, ISSN 1560-3547
Publisher: Turpion - Moscow Ltd.
DOI: 10.1134/s1560354722060107

Deformational rigidity of integrable metrics on the torus

Author(s): JOSCHA HENHEIK
Published in: Ergodic Theory and Dynamical Systems, Issue 45, 2025, Page(s) 467-503, ISSN 0143-3857
Publisher: Cambridge University Press
DOI: 10.1017/etds.2024.48

On some invariants of Birkhoff billiards under conjugacy

Author(s): Koudjinan E, Kaloshin V.
Published in: Regular and Chaotic Dynamics, Issue 27(6), 2022, Page(s) 525-537, ISSN 1560-3547
Publisher: Turpion - Moscow Ltd.
DOI: 10.1134/s1560354722050021

Birkhoff Conjecture for Nearly Centrally Symmetric Domains

Author(s): V. Kaloshin, C. E. Koudjinan, Ke Zhang
Published in: Geometric and Functional Analysis, Issue 34, 2024, Page(s) 1973-2007, ISSN 1016-443X
Publisher: Birkhauser Verlag
DOI: 10.1007/s00039-024-00695-6

Book chapters (1)

Lecture Notes on Birkhoff Billiards: Dynamics, Integrability and Spectral Rigidity

Author(s): Corentin Fierobe, Vadim Kaloshin, Alfonso Sorrentino
Published in: Lecture Notes in Mathematics, Modern Aspects of Dynamical Systems, 2024, Page(s) 1-57
Publisher: Springer Nature Switzerland
DOI: 10.1007/978-3-031-62014-0_1