Communications in Mathematical Physics

, Volume 143, Issue 3, pp 431–449

Dual polygonal billiards and necklace dynamics

Authors

  • Eugene Gutkin
    • Department of MathematicsUniversity of Southern California
  • Nandor Simanyi
    • Department of MathematicsUniversity of Southern California
Article

DOI: 10.1007/BF02099259

Cite this article as:
Gutkin, E. & Simanyi, N. Commun.Math. Phys. (1992) 143: 431. doi:10.1007/BF02099259

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.

Copyright information

© Springer-Verlag 1992