, Volume 143, Issue 3, pp 431-449

Dual polygonal billiards and necklace dynamics

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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.

Partially supported by NSF Grant DMS 88-02643
Communicated by J. N. Mather