Volume 3, issue 2 (2003)

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On three-periodic trajectories of multi-dimensional dual billiards

Serge Tabachnikov

Algebraic & Geometric Topology 3 (2003) 993–1004
 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 2000
Primary: 37J45, 70H12
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/