Invariant tori in Hamiltonian systems with impacts

Research output: Contribution to journalArticlepeer-review


It is shown that a large class of solutions in two-degree-of-freedom Hamiltonian systems of billiard type can be described by slowly varying one-degree-of-freedom Hamiltonian systems. Under some non-degeneracy conditions such systems are found to possess a large set of quasiperiodic solutions filling out two dimensional tori, which correspond to caustics in the classical billiard. This provides a unified proof of existence of quasiperiodic solutions in convex billiards and other systems with impacts including classical billiard in electric and magnetic fields, dual billiard, and Fermi-Ulam systems.

Original languageEnglish (US)
Pages (from-to)289-302
Number of pages14
JournalCommunications in Mathematical Physics
Issue number2
StatePublished - 2000
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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