Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards

Academic Article


  • The Local Ergodic Theorem (also known as the 'Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However, the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of the Local Ergodic Theorem for two dimensional billiards without using the Ansatz. © 2010 Springer Science+Business Media, LLC.
  • Authors

    Published In

    Digital Object Identifier (doi)

    Author List

  • Chernov N; Simányi N
  • Start Page

  • 355
  • End Page

  • 366
  • Volume

  • 139
  • Issue

  • 3