On some invariants of Birkhoff billiards under conjugacy

DOI10.1134/S1560354722050021MaRDI QIDQ2093114

Comlan E. Koudjinan, Vadim Yu. Kaloshin

Publication date: 4 November 2022

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.14640

zbMATH Keywords

conjugacyintegrabilityBirkhoff billiardMarvizi-Melrose invariantsMather's \(\beta\)-function

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Relations of finite-dimensional Hamiltonian and Lagrangian systems with topology, geometry and differential geometry (symplectic geometry, Poisson geometry, etc.) (37J39) Dynamical systems with singularities (billiards, etc.) (37C83)

Related Items (1)

Marked length spectral determination of analytic chaotic billiards with axial symmetries

Uses Software

• Mathematica

Cites Work

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• Computing Mather's \(\beta\)-function for Birkhoff billiards
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• The principle of least action in geometry and dynamics
• Elliptical billiards and Poncelet’s theorem
• Differentiability of the minimal average action as a function of the rotation number
• Strange Billiard Tables
• Invariant Tori for the Billiard Ball Map
• Semiclassical transition from an elliptical to an oval billiard

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