Dual polygonal billiards and necklace dynamics |
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| Authors: | Eugene Gutkin Nandor Simanyi |
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| Institution: | (1) Department of Mathematics, University of Southern California, 90089 Los Angeles, CA, USA;(2) Present address: Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364 Budapest, Hungary |
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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 |
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