Proof of the ergodic hypothesis for typical hard ball systems

Academic Article

Abstract

  • We consider the system of N (≥ 2) hard balls with masses m1,...,mNand radius r in the flat torus double-struck T signLν= ℝν/L · ℤνof size L, ν ≥ 3. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost every selection (m1,...,mN; L) of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the case ν = 2. The method of that proof was primarily dynamical-geometric, whereas the present approach is inherently algebraic.
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    Digital Object Identifier (doi)

    Start Page

  • 203
  • End Page

  • 233
  • Volume

  • 5
  • Issue

  • 2