Periodic billiard orbits are dense in rational polygons

DOI10.1090/S0002-9947-98-02089-3zbMath0910.58013OpenAlexW1569747394MaRDI QIDQ4211110

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Publication date: 10 September 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-02089-3

zbMATH Keywords

periodic orbitsrational polygonsbillard flow

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99)

Related Items (20)

Holonomy limits of complex projective structures ⋮ Trajectory tracking of a bouncing ball in a triangular billiard by unfolding and folding the billiard table ⋮ Unnamed Item ⋮ Minimality of the Ehrenfest wind-tree model ⋮ On the mathematical transport theory in microporous media: the billiard approach ⋮ Cylinder curves in finite holonomy flat metrics ⋮ Topologically weakly mixing polygonal billiards ⋮ Polygonal Billiards with Strongly Contractive Reflection Laws: A Review of Some Hyperbolic Properties ⋮ Survey lecture on billiards ⋮ \(C^1\)-generic billiard tables have a dense set of periodic points ⋮ Homotopical rigidity of polygonal billiards ⋮ Billiard in a triangle and quadratic homogeneous foliations on \(\mathbb C^{2}\) ⋮ The existence of a billiard orbit in the regular hyperbolic simplex ⋮ Equidistribution of saddle connections on translation surfaces ⋮ Periodic billiard orbits in right triangles. ⋮ Billiards in polygons and homogeneous foliations on C² ⋮ Existence of closed geodesics through a regular point on translation surfaces ⋮ Diffusion and escape from polygonal channels: extreme values and geometric effects ⋮ Some open problems in low dimensional dynamical systems ⋮ Computer-Assisted Methods for Analyzing Periodic Orbits in Vibrating Gravitational Billiards

Cites Work

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• Unnamed Item
• Erratum to: ``Teichmüller curves in moduli space, Eisenstein series and an application to triangular billiards
• A condition for minimal interval exchange maps to be uniquely ergodic
• Ergodicity of billiard flows and quadratic differentials
• The billiard in a regular polygon
• Closed trajectories for quadratic differentials with an application to billiards
• Local instability of orbits in polygonal and polyhedral billiards
• The growth rate of trajectories of a quadratic differential
• Billiards on almost integrable polyhedral surfaces
• Billiards and Rational Periodic Directions in Polygons
• Billiards in polygons
• Billiards in polygons
• Interval exchange transformations

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