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Discrete analog of the projective equivalence and integrable billiard tables

Published online by Cambridge University Press:  01 October 2008

G. POPOV  and
P. TOPALOV
G. POPOV
Affiliation:
Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44072 Nantes Cedex 03, France (email: georgi.popov@math.univ-nantes.fr)
P. TOPALOV
Affiliation:
Department of Mathematics, Northeastern University, 360 Huntington Avenue,Boston, MA 02115, USA
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Abstract

A class of discrete dynamical systems called projectively (or geodesically) equivalent Lagrangian systems is defined. We prove that these systems admit families of integrals. In the case of geodesically equivalent billiard tables, these integrals are pairwise commuting. We describe a family of geodesically equivalent billiard tables on surfaces of constant curvature. This is a special case of the so-called ‘Liouville billiard tables’.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 5 , October 2008 , pp. 1657 - 1684
Copyright
Copyright © 2008 Cambridge University Press

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