Algebraic and Geometric Topology 3 (2003), paper no. 33, pages 993-1004.

On three-periodic trajectories of multi-dimensional dual billiards

Serge Tabachnikov

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 and Lusternik-Schnirelman theory

AMS subject classification. Primary: 37J45, 70H12.

DOI: 10.2140/agt.2003.3.993

E-print: arXiv:math.DS/0302254

Submitted: 21 Febuary 2003. Accepted: 23 September 2003. Published: 5 October 2003.

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Serge Tabachnikov
Department of Mathematics
Pennsylvania State University
University Park, PA 16802, USA
Email: tabachni@math.psu.edu
URL: http://www.math.psu.edu/tabachni
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