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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.

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Author notes

  1. Nandor Simanyi

    Present address: Mathematical Institute of the Hungarian Academy of Sciences, P.O. Box 127, H-1364, Budapest, Hungary

Authors and Affiliations

  1. Department of Mathematics, University of Southern California, 90089, Los Angeles, CA, USA

    Eugene Gutkin & Nandor Simanyi

Authors
  1. Eugene Gutkin
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  2. Nandor Simanyi
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Additional information

Communicated by J. N. Mather

Partially supported by NSF Grant DMS 88-02643

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Gutkin, E., Simanyi, N. Dual polygonal billiards and necklace dynamics. Commun.Math. Phys. 143, 431–449 (1992). https://doi.org/10.1007/BF02099259

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  • DOI: https://doi.org/10.1007/BF02099259

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