Billiard trajectories in regular polygons and geodesics on regular polyhedra

DOI10.1007/s40598-020-00170-8zbMath1491.53053OpenAlexW3118433553MaRDI QIDQ2066760

Dmitry Fuchs

Publication date: 14 January 2022

Published in: Arnold Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40598-020-00170-8

zbMATH Keywords

geodesicsdodecahedronbilliard trajectorieshyperbolic dodecaherdonparallel trajectoriesshort trajectories

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Geodesics in global differential geometry (53C22) Polyhedral manifolds (52B70) Flows on surfaces (37E35)

Cites Work

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• Geodesics on the regular tetrahedron and the cube
• Geodesics on regular polyhedra with endpoints at the vertices
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• Regular tessellations of surfaces and (p,q,2)-triangle groups
• The billiard in a regular polygon
• Topological transitivity of billiards in polygons
• Billiard dynamics: a survey with the emphasis on open problems
• On a triply periodic polyhedral surface whose vertices are Weierstrass points
• Periodic billiard trajectories in regular polygons and closed geodesics on regular polyhedra
• Billiard dynamics: An updated survey with the emphasis on open problems
• A Trajectory from a Vertex to Itself on the Dodecahedron
• Calculation of Fuchsian groups associated to billiards in a rational triangle

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