Entropy of billiard maps and a dynamical version of the Birkhoff conjecture

DOI10.1016/J.GEOMPHYS.2017.11.012zbMath1388.37043OpenAlexW2774511787WikidataQ122880638 ScholiaQ122880638MaRDI QIDQ1742292

Jean-Pierre Marco

Publication date: 11 April 2018

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2017.11.012

zbMATH Keywords

complexityintegrabilitybilliardpolynomial entropy

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (9)

On polynomially integrable Birkhoff billiards on surfaces of constant curvature ⋮ Polynomial entropy of amenable group actions for noncompact sets ⋮ Rigidity and flexibility of polynomial entropy ⋮ Variational principle for polynomial entropy on subsets of free semigroup actions ⋮ Polynomial entropy of subsets for free semigroup actions ⋮ A survey on polynomial in momenta integrals for billiard problems ⋮ Automorphisms of compact Kähler manifolds with slow dynamics ⋮ Categorical polynomial entropy ⋮ Polynomial entropy of nonautonomous dynamical systems for noncompact sets

Cites Work

• An integrable deformation of an ellipse of small eccentricity is an ellipse
• Convex billiards and a theorem by E. Hopf
• Two applications of Jacobi fields to the billiard ball problem
• On the local Birkhoff conjecture for convex billiards
• Flat metrics are strict local minimizers for the polynomial entropy
• Tonelli Hamiltonians without conjugate points and \(C^0\) integrability
• Polynomial entropies for Bott integrable Hamiltonian systems
• An entropic characterization of the flat metrics on the two torus
• Glancing billiards
• Classical solutions for a free particle in a confocal elliptic billiard
• Monotone twist mappings and the calculus of variations
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