Billiard dynamics: a survey with the emphasis on open problems

DOI10.1070/RD2003v008n01ABEH000222zbMath1023.37022OpenAlexW4236181003MaRDI QIDQ1407950

Eugene Gutkin

Publication date: 14 September 2003

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1070/rd2003v008n01abeh000222

zbMATH Keywords

periodic orbitsintegrabilitybilliardhyperbolic dynamics

Mathematics Subject Classification ID

Low-dimensional dynamical systems (37E99) Hamiltonian and Lagrangian mechanics (70H99)

Related Items (26)

Addendum to: ``Capillary floating and the billiard ball problem ⋮ On recurrence and ergodicity for geodesic flows on non-compact periodic polygonal surfaces ⋮ On the local Birkhoff conjecture for convex billiards ⋮ Description of singularities for system ``billiard in an ellipse ⋮ Algebra and Geometry Through Hamiltonian Systems ⋮ Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces ⋮ Numerical exploration of a hexagonal string billiard ⋮ On the integrability of Birkhoff billiards ⋮ Nearly circular domains which are integrable close to the boundary are ellipses ⋮ The existence of a billiard orbit in the regular hyperbolic simplex ⋮ Description of singularities for billiard systems bounded by confocal ellipses or hyperbolas ⋮ Billiard dynamics: An updated survey with the emphasis on open problems ⋮ A single particle impact model for motion in avalanches ⋮ Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards ⋮ Capillary floating and the billiard ball problem ⋮ On the chaotic behavior of non-flat billiards ⋮ Topological entropy and blocking cost for geodesics in Riemannian manifolds ⋮ Topological type of isoenergy surfaces of billiard books ⋮ Growth rates for geometric complexities and counting functions in polygonal billiards ⋮ Billiard trajectories in regular polygons and geodesics on regular polyhedra ⋮ On the integrability of strictly convex billiard tables with boundaries close to ellipses with small eccentricities ⋮ Book Review: Chaotic billiards ⋮ Topology of Liouville foliations of integrable billiards on table-complexes ⋮ Dual billiards ⋮ Non-persistence of resonant caustics in perturbed elliptic billiards ⋮ Inverse problems and rigidity questions in billiard dynamics

This page was built for publication: Billiard dynamics: a survey with the emphasis on open problems