Communications in Mathematical Physics

, Volume 143, Issue 3, pp 431–449

Dual polygonal billiards and necklace dynamics

  • Eugene Gutkin
  • Nandor Simanyi

DOI: 10.1007/BF02099259

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


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

Authors and Affiliations

  • Eugene Gutkin
    • 1
  • Nandor Simanyi
    • 1
  1. 1.Department of MathematicsUniversity of Southern CaliforniaLos AngelesUSA
  2. 2.Mathematical Institute of the Hungarian Academy of SciencesBudapestHungary