On three-periodic trajectories of multi-dimensional dual billiards

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

Keywords

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

Mathematical Subject Classification 2000

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/

Volume 3, issue 2 (2003)

Serge Tabachnikov