A dynamical approach to symplectic and spectral invariants for billiards

DOI10.1007/BF02096834zbMath0786.58034OpenAlexW1990825718MaRDI QIDQ1801539

Edoh Y. Amiran

Publication date: 6 May 1994

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02096834

zbMATH Keywords

invariantclosed geodesicscausticsboundary mapbilliard ball mapLazutkin parameter

Mathematics Subject Classification ID

Topological dynamics (37B99) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) General geometric structures on manifolds (almost complex, almost product structures, etc.) (53C15)

Related Items (4)

Aubry-Mather theory and the inverse spectral problem for planar convex domains ⋮ Duality of caustics in Minkowski billiards ⋮ Noncoincidence of geodesic lengths and hearing elliptic quantum billiards ⋮ One can hear the shape of ellipses of small eccentricity

Cites Work

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• Caustics and evolutes for convex planar domains
• The Poisson summation formula for manifolds with boundary
• Spectral invariants of convex planar regions
• The spectrum of positive elliptic operators and periodic bicharacteristics
• Equivalence of glancing hyper-surfaces
• The propagation of singularities along gliding rays
• Formule de Poisson pour les variétés riemanniennes
• Curvature and the eigenvalues of the Laplacian
• The isoperimetric inequality
• THE EXISTENCE OF CAUSTICS FOR A BILLIARD PROBLEM IN A CONVEX DOMAIN
• Can One Hear the Shape of a Drum?

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