Elliptic islands appearing in near-ergodic flows

Dmitry Turaev, Vered Rom-Kedar

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

It is proved that periodic and homoclinic trajectories which are tangent to the boundary of any scattering (ergodic) billiard produce elliptic islands in the 'nearby' Hamiltonian flows i.e. in a family of two-degrees-of-freedom smooth Hamiltonian flows which converge to the singular billiard flow smoothly where the billiard flow is smooth and continuously where it is continuous. Such Hamiltonians exist; indeed, sufficient conditions are supplied, and thus it is proved that a large class of smooth Hamiltonians converges to billiard flows in this manner. These results imply that ergodicity may be lost in the physical setting, where smooth Hamiltonians which are arbitrarily close to the ergodic billiards, arise.

Original languageEnglish
Pages (from-to)575-600
Number of pages26
JournalNonlinearity
Volume11
Issue number3
DOIs
StatePublished - 1 May 1998
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Physics and Astronomy (all)
  • Applied Mathematics

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