Asymptotic dynamics of the dual billiard transformation

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Abstract

Given a strictly convex plane curve, the dual billiard transformation is the transformation of its exterior defined as follows: given a point x outside the curve, draw a support line to it from the point and reflect x at the support point. We show that the dual billiard transformation far from the curve is well approximated by the time 1 transformation of a Hamiltonian flow associated with the curve.

Original languageEnglish (US)
Pages (from-to)27-37
Number of pages11
JournalJournal of Statistical Physics
Volume83
Issue number1-2
DOIs
StatePublished - Apr 1996

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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