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Discrete analog of the projective equivalence and integrable billiard tables
Published online by Cambridge University Press: 01 October 2008
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’.
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- Copyright © 2008 Cambridge University Press
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