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On smooth Hamiltonian flows limited to ergodic billiards

  • Dmitry TuraevEmail author
  • Vered Rom-Kedar
Dynamics And Chaos
Part of the Lecture Notes in Physics book series (LNP, volume 511)

Abstract

Sufficient conditions are found so that a family of smooth Hamiltonian flows limits to a billiard flow as a parameter ɛ→0. This limit is proved to be C 1 near non-singular orbits and C 0 near orbits tangent to the billiard boundary. These results are used to prove that scattering (thus ergodic) billiards with tangent periodic orbits or tangent homoclinic orbits produce nearby Hamiltonian flows with elliptic islands. This implies that ergodicity may be lost for smooth potentials which are arbitrarily close to ergodic billiards. Thus, in some cases, anomoulous transport associated with stickiness to stability islands is expected

AMS No.

58F15 82C05 34C37 58F05 58F13 58F14 

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Copyright information

© Springer-Verlag 1998

Authors and Affiliations

  1. 1.The Department of Applied Mathematics and Computer ScienceThe Weizmann Institute of ScienceRehovotIsrael

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