Annales Henri Poincaré

, Volume 5, Issue 2, pp 203–233

Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

Open AccessOriginal paper

DOI: 10.1007/s00023-004-0166-8

Cite this article as:
Simányi, N. Ann. Henri Poincaré (2004) 5: 203. doi:10.1007/s00023-004-0166-8

Abstract.

We consider the system of \( N (\geq 2) \) hard balls with masses \( m_{1}, \ldots, m_{N} \) and radius r in the flat torus \( \mathbb{T}_{L}^{\nu} = \mathbb{R}^{\nu} / L \cdot \mathbb{Z}^{\nu} \) of size \( L, \nu \geq 3 \) . We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost every selection \( (m_{1}, \ldots, m_{N}; L) \) of the outer geometric parameters. This theorem complements my earlier result that proved the same, almost sure ergodicity for the case \( \nu = 2 \) . The method of that proof was primarily dynamical-geometric, whereas the present approach is inherently algebraic.

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© Birkhäuser-Verlag 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA