Communications in Mathematical Physics

, Volume 143, Issue 3, pp 431–449 | Cite as

Dual polygonal billiards and necklace dynamics

  • Eugene Gutkin
  • Nandor Simanyi
Article

Abstract

We study the orbits of the dual billiard map about a polygonal table using the technique of necklace dynamics. Our main result is that for a certain class of tables, called the quasi-rational polygons, the dual billiard orbits are bounded. This implies that for the subset of rational tables (i.e. polygons with rational vertices) the dual billiard orbits are periodic.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Eugene Gutkin
    • 1
  • Nandor Simanyi
    • 1
  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA

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