Skip to main content
Springer Nature Link
Log in

Topological transitivity of billiards in polygons

  • Published:
Mathematical notes of the Academy of Sciences of the USSR Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature cited

  1. Ya. G. Sinai, Introduction to Ergodic Theory [in Russian], Erevan University Press, Erevan (1973).

    Google Scholar 

  2. A. G. Maier, “Trajectories on orientable surfaces,” Matem. Sbornik,12 (54), No. 1, 71–84 (1943).

    Google Scholar 

  3. A. B. Katok, “Invariant measures of flows on orientable surfaces,” Dokl. Akad. Nauk SSSR,211, No. 4, 775–778 (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    A. N. Zemlyakov & A. B. Katok

  2. Central Economicomathematical Institute, Academy of Sciences of the USSR, USSR

    A. N. Zemlyakov & A. B. Katok

Authors
  1. A. N. Zemlyakov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. B. Katok
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 18, No. 2, pp. 291–300, August, 1975.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zemlyakov, A.N., Katok, A.B. Topological transitivity of billiards in polygons. Mathematical Notes of the Academy of Sciences of the USSR 18, 760–764 (1975). https://doi.org/10.1007/BF01818045

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01818045

Keywords

Search

Navigation