Topological transitivity of billiards in polygons

A. N. Zemlyakov; Anatoly Katok

doi:10.1007/BF01818045

Topological transitivity of billiards in polygons

A. N. Zemlyakov, Anatoly Katok

Research output: Contribution to journal › Article › peer-review

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Abstract

Consider a billiard in a polygon Q⊂R² having all angles commensurate with π. For the majority of initial directions, density of every infinite semitrajectory in configuration space is proved. Also proved is the typicality of polygons for which some billiard trajectory is dense in phase space.

Original language	English (US)
Pages (from-to)	760-764
Number of pages	5
Journal	Mathematical Notes of the Academy of Sciences of the USSR
Volume	18
Issue number	2
DOIs	https://doi.org/10.1007/BF01818045
State	Published - Aug 1 1975

All Science Journal Classification (ASJC) codes

Mathematics(all)

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10.1007/BF01818045

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title = "Topological transitivity of billiards in polygons",

abstract = "Consider a billiard in a polygon Q⊂R2 having all angles commensurate with π. For the majority of initial directions, density of every infinite semitrajectory in configuration space is proved. Also proved is the typicality of polygons for which some billiard trajectory is dense in phase space.",

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AU - Katok, Anatoly

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AB - Consider a billiard in a polygon Q⊂R2 having all angles commensurate with π. For the majority of initial directions, density of every infinite semitrajectory in configuration space is proved. Also proved is the typicality of polygons for which some billiard trajectory is dense in phase space.

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JO - Mathematical Notes of the Academy of Sciences of the USSR

JF - Mathematical Notes of the Academy of Sciences of the USSR

IS - 2

ER -

Topological transitivity of billiards in polygons

Abstract

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