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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Periodic billiard orbits are dense
in rational polygons


Authors: M. Boshernitzan, G. Galperin, T. Krüger and S. Troubetzkoy
Journal: Trans. Amer. Math. Soc. 350 (1998), 3523-3535
MSC (1991): Primary 58F05
MathSciNet review: 1458298
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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 $\pi.$


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Additional Information

M. Boshernitzan
Affiliation: Department of Mathematics, Rice University, Houston, Texas 77005
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
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
Email: troubetz@math.uab.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02089-3
PII: S 0002-9947(98)02089-3
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.
Article copyright: © Copyright 1998 American Mathematical Society