Topological transitivity of billiards in polygons

A. N. Zemlyakov, Anatoly Katok

Research output: Contribution to journalArticle

95 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)760-764
Number of pages5
JournalMathematical Notes of the Academy of Sciences of the USSR
Volume18
Issue number2
DOIs
StatePublished - Aug 1 1975

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Topological Transitivity
Billiards
Polygon
Configuration Space
Phase Space
Trajectory
Angle

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

Zemlyakov, A. N. ; Katok, Anatoly. / Topological transitivity of billiards in polygons. In: Mathematical Notes of the Academy of Sciences of the USSR. 1975 ; Vol. 18, No. 2. pp. 760-764.
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Topological transitivity of billiards in polygons. / Zemlyakov, A. N.; Katok, Anatoly.

In: Mathematical Notes of the Academy of Sciences of the USSR, Vol. 18, No. 2, 01.08.1975, p. 760-764.

Research output: Contribution to journalArticle

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