Noncoincidence of geodesic lengths and hearing elliptic quantum billiards

DOI10.1007/BF02174214zbMath0929.37007OpenAlexW2001635464MaRDI QIDQ1285271

Edoh Y. Amiran

Publication date: 2 February 2000

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02174214

zbMATH Keywords

geodesicsbilliardsstrictly convexspectral invariantsellipsesinvariant circlesbilliard ball maplengths of closed geodesicslengths of invariant circlesstrong noncoincidence condition

Mathematics Subject Classification ID

Estimates of eigenvalues in context of PDEs (35P15) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (1)

One can hear the shape of ellipses of small eccentricity

Cites Work

• 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
• Invariants of the length spectrum and spectral invariants of planar convex domains
• A dynamical approach to symplectic and spectral invariants for billiards
• Formule de Poisson pour les variétés riemanniennes
• THE EXISTENCE OF CAUSTICS FOR A BILLIARD PROBLEM IN A CONVEX DOMAIN

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