Communications in Mathematical Physics

, Volume 110, Issue 4, pp 625–640

Global stability of a class of discontinuous dual billiards

  • Franco Vivaldi
  • Anna V. Shaidenko

DOI: 10.1007/BF01205552

Cite this article as:
Vivaldi, F. & Shaidenko, A.V. Commun.Math. Phys. (1987) 110: 625. doi:10.1007/BF01205552


An infinite-parameter family of discontinuous area-preserving maps is studied, using geometrical methods. Necessary and sufficient conditions are determined for the existence of some bounding invariant sets, which guarantee global stability. It is shown that under some additional constraints, all orbits become periodic, most of them Lyapounov stable, and with a maximal period in any bounded domain of phase space. This yields a class of maps acting on a discrete phase space.

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • Franco Vivaldi
    • 1
  • Anna V. Shaidenko
    • 2
  1. 1.School of Mathematical SciencesQueen Mary CollegeLondonEngland
  2. 2.Department of MathematicsNovosibirskUSSR