An estimate from above of the number of periodic orbits for semi- dispersed billiards

DOI10.1007/BF01219195zbMath0819.58032MaRDI QIDQ1812722

Latchezar Stoyanov

Publication date: 25 June 1992

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

zbMATH Keywords

periodic pointsexponential estimatebilliard ball mapsemi-dispersed billiards

Mathematics Subject Classification ID

Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (15)

Anti-integrability in scattering billiards ⋮ Variational principle for periodic trajectories of hyperbolic billiards ⋮ DIMENSIONAL CHARACTERISTICS OF THE NONWANDERING SETS OF OPEN BILLIARDS ⋮ Rotation sets of billiards with one obstacle ⋮ Entropy rigidity for 3D conservative Anosov flows and dispersing billiards ⋮ On topological entropy of billiard tables with small inner scatterers ⋮ Advanced statistical properties of dispersing billiards ⋮ Billiard dynamics: An updated survey with the emphasis on open problems ⋮ Rotation sets of billiards with \(N\) obstacles on a torus ⋮ On the measure of maximal entropy for finite horizon Sinai Billiard maps ⋮ Topological entropy and periodic points of two-dimensional hyperbolic billiards ⋮ Entropy formula for systems with inducing schemes ⋮ Billiards in the \(l^p\) unit balls of the plane. ⋮ Number of nodal domains of eigenfunctions on non-positively curved surfaces with concave boundary ⋮ Differentiability of Hausdorff dimension of the non-wandering set in a planar open billiard

Cites Work

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• Principles for the design of billiards with nonvanishing Lyapunov exponents
• The growth rate for the number of singular and periodic orbits for a polygonal billiard
• Decay of solutions of the wave equation in the exterior of several convex bodies
• Precise informations on the poles of the scattering matrix for two strictly convex obstacles
• Invariant manifolds, entropy and billiards; smooth maps with singularities. With the collab. of F. Ledrappier and F. Przytycki
• Lyapunov exponents, entropy and periodic orbits for diffeomorphisms
• Applications of ergodic theory to the investigation of manifolds of negative curvature
• On the number of periodic reflecting rays in generic domains
• Dynamical systems with elastic reflections

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