The Symbolic Representation of Billiards without Boundary Condition

DOI10.2307/2001649zbMath0731.58055OpenAlexW4249924092MaRDI QIDQ3357158

Takehiko Morita

Publication date: 1991

Full work available at URL: https://doi.org/10.2307/2001649

zbMATH Keywords

dynamical systembilliard problemsymbolic flow

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Low-dimensional dynamical systems (37E99) Dynamical systems with hyperbolic behavior (37D99)

Related Items (17)

Generic properties of open billiards ⋮ Pointwise rotation sets of dispersing billiards ⋮ Periodic orbits of a dynamical system in a compound central field and a perturbed billiards system ⋮ Differentiability of the largest Lyapunov exponent for planar open billiards ⋮ Catching all geodesics of a manifold with moving balls and application to controllability of the wave equation ⋮ Marked length spectral determination of analytic chaotic billiards with axial symmetries ⋮ Projective cones for sequential dispersing billiards ⋮ Closed billiards trajectories with prescribed bounces ⋮ Singular perturbation of symbolic dynamics via thermodynamic formalism ⋮ Entropy rigidity for 3D conservative Anosov flows and dispersing billiards ⋮ Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards ⋮ On general rotation sets of open billiards ⋮ Meromorphic extensions of a class of zeta functions for two-dimensional billiards without eclipse ⋮ On topological entropy of billiard tables with small inner scatterers ⋮ Distribution of closed orbits of billiard flows on the plane ⋮ Topological entropy and periodic points of two-dimensional hyperbolic billiards ⋮ Differentiability of Hausdorff dimension of the non-wandering set in a planar open billiard

Cites Work

• Unnamed Item
• An analogue of the prime number theorem for closed orbits of Axiom A flows
• On the existence of the poles of the scattering matrix for several convex bodies
• Singular perturbation of symbolic flows and poles of the zeta functions
• The Poisson summation formula for manifolds with boundary
• Perturbed billiard systems, I. The ergodicity of the motion of a particle in a compound central field

This page was built for publication: The Symbolic Representation of Billiards without Boundary Condition