Conditional proof of the boltzmann-Sinai ergodic hypothesis

Academic Article

Abstract

  • We consider the system of N (≥ 2) elastically colliding hard balls of masses m1, ⋯ ,Nand radius r on the flat unit torus Tν, ν≥2. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i.e. the full hyperbolicity and ergodicity of such systems for every selection (m1, ⋯ ,mN; r) of the external parameters, provided that almost every singular orbit is geometrically hyperbolic (sufficient), i.e. the so called Chernov-Sinai Ansatz is true. The present proof does not use the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools from geometric analysis. © 2009 Springer-Verlag.
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    Start Page

  • 381
  • End Page

  • 413
  • Volume

  • 177
  • Issue

  • 2