Big islands in dispersing billiard-like potentials

Vered Rom-Kedar, Dmitry Turaev

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


We derive a rigorous estimate of the size of islands (in both phase space and parameter space) appearing in smooth Hamiltonian approximations of scattering billiards. The derivation includes the construction of a local return map near singular periodic orbits for an arbitrary scattering billiard and for the general smooth billiard potentials. Thus, universality classes for the local behavior are found. Moreover, for all scattering geometries and for many types of natural potentials which limit to the billiard flow as a parameter ∈ → 0, islands of polynomial size in ∈ appear. This suggests that the loss of ergodicity via the introduction of the physically relevant effect of smoothening of the potential in modeling, for example, scattering molecules, may be of physically noticeable effect.

Original languageEnglish
Pages (from-to)187-210
Number of pages24
JournalPhysica D: Nonlinear Phenomena
Issue number3-4
StatePublished - 15 Jun 1999
Externally publishedYes


  • Elliptic islands
  • Ergodicity
  • Mixed dynamics
  • Singular Hamiltonian systems

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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