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On three-periodic trajectories of multi-dimensional dual billiards

Serge Tabachnikov

Algebraic & Geometric Topology 3 (2003) 993–1004

DOI: 10.2140/agt.2003.3.993

arXiv: math.DS/0302254
Abstract

We consider the dual billiard map with respect to a smooth strictly convex closed hypersurface in linear 2m–dimensional symplectic space and prove that it has at least 2m distinct 3–periodic orbits.

Keywords

dual billiards, symplectic relation, periodic orbits, Morse, Lusternik–Schnirelman theory
Mathematical Subject Classification

Primary: 37J45, 70H12
References
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Publication

Received: 21 2003
Accepted: 23 September 2003
Published: 5 October 2003
Authors
Serge Tabachnikov
Department of Mathematics
Pennsylvania State University
University Park PA 16802
USA
http://www.math.psu.edu/tabachni/