On the number of periodic reflecting rays in generic domains

DOI10.1017/S0143385700004338zbMath0668.58005MaRDI QIDQ3821308

Vesselin Petkov, Latchezar Stoyanov

Publication date: 1988

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Mathematics Subject Classification ID

General theory of differentiable manifolds (58A99)

Related Items (11)

Convex billiards on convex spheres ⋮ Spectrum of the Poincaré map for periodic reflecting rays in generic domains ⋮ Unnamed Item ⋮ Billiards in generic convex bodies have positive topological entropy ⋮ Quantum ergodic restriction theorems. I: Interior hypersurfaces in domains with ergodic billiards ⋮ Double normals of most convex bodies ⋮ Equidistribution of phase shifts in obstacle scattering ⋮ Billiard dynamics: An updated survey with the emphasis on open problems ⋮ A bumpy metric theorem and the Poisson relation for generic strictly convex domains ⋮ An estimate from above of the number of periodic orbits for semi- dispersed billiards ⋮ Expansiveness and hyperbolicity in convex billiards

Cites Work

• Spectrum of the Poincaré map for periodic reflecting rays in generic domains
• Applications of ergodic theory to the investigation of manifolds of negative curvature
• Periodic geodesics of generic nonconvex domains in 𝐑² and the Poisson relation
• Periods of Multiple Reflecting Geodesics and Inverse Spectral Results
• High frequency asymptotics of the scattering amplitude for non-convex bodies
• Singularities of boundary value problems. I

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