Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

Details Proof of the Ergodic Hypothesis for Typical Hard Ball Systems Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

2002-10-17

arxiv.org/abs/math/0210280v2

Annales Henri Poincar\'e 5 (2004), pp. 203-233

Mathematics

Dynamical Systems

31 pages, no figures

Scientific paper

10.1007/s00023-004-0166-8

We consider the system of $N$ ($\ge2$) hard balls with masses $m_1,...,m_N$ and radius $r$ in the flat torus $\Bbb T_L^\nu=\Bbb R^\nu/L\cdot\Bbb Z^\nu$ of size $L$, $\nu\ge3$. We prove the ergodicity (actually, the Bernoulli mixing property) of such systems for almost every selection $(m_1,...,m_N; L)$ 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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