Dual polygonal billiards and necklace dynamics
- Cite this article as:
- Gutkin, E. & Simanyi, N. Commun.Math. Phys. (1992) 143: 431. doi:10.1007/BF02099259
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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.