Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

Abstract

We consider the system of $N$ ($\ge 2$) hard balls with masses $m_1,...,m_N$ and radius $r$ in the flat torus ${\mathbb{T}}_L^{\nu }={\mathbb{R}}^{\nu }/L\cdot {\mathbb{Z}}^{\nu }$ of size $L$, $\nu \ge 3$. 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.

31 pages, no figures

References in corpus (1)

• Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

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