Journal of Statistical Physics

, Volume 83, Issue 1–2, pp 27–37 | Cite as

Asymptotic dynamics of the dual billiard transformation

  • Serge Tabachnikov
Articles
Received:
Accepted:

Abstract

Given a strictly convex plane curve, the dual billiard transformation is the transformation of its exterior defined as follows: given a pointx outside the curve, draw a support line to it from the point and reflectx 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.

Key Words

Dual billiards Hamiltonian flow KAM theory invariant curves 
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Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Serge Tabachnikov
    • 1
    • 2
  1. 1.University of ArkansasFayetteville
  2. 2.Wolfson College and I. Newton InstituteUniversity of CambridgeCambridgeEngland

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