Periodic billiard orbits are dense in rational polygons
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- by M. Boshernitzan, G. Galperin, T. Krüger and S. Troubetzkoy
- Trans. Amer. Math. Soc. 350 (1998), 3523-3535
- DOI: https://doi.org/10.1090/S0002-9947-98-02089-3
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Abstract:
We show that periodic orbits are dense in the phase space for billiards in polygons for which the angle between each pair of sides is a rational multiple of $\pi .$References
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Bibliographic Information
- M. Boshernitzan
- Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005
- MR Author ID: 39965
- Email: michael@math.rice.edu
- G. Galperin
- Affiliation: Forschungszentrum BiBos, Universität Bielefeld, Bielefeld, Germany
- Address at time of publication: Department of Mathematics, Eastern Illinois University
- MR Author ID: 70890
- Email: cfgg@eiu.edu
- T. Krüger
- Affiliation: Forschungszentrum BiBos, Universität Bielefeld, Bielefeld, Germany
- S. Troubetzkoy
- Affiliation: Forschungszentrum BiBos, Universität Bielefeld, Bielefeld, Germany and Institute for Mathematical Science, SUNY at Stony Brook, Stony Brook, New York 11794
- Address at time of publication: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294
- MR Author ID: 292399
- Email: troubetz@math.uab.edu
- Received by editor(s): July 29, 1996
- Additional Notes: MB is partially supported by NSF-DMS-9224667.
GG thanks the Alexander von Humboldt Stiftung for their support.
ST thanks the Deutsche Forschungsgemeinschaft for their support. - © Copyright 1998 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 350 (1998), 3523-3535
- MSC (1991): Primary 58F05
- DOI: https://doi.org/10.1090/S0002-9947-98-02089-3
- MathSciNet review: 1458298