Proof of the Ergodic Hypothesis for Typical Hard Ball Systems

Abstract

We consider the system of $N$ ($\ge2$) hard balls with masses $m_1,...,m_N$ and radius $r$ in the flat torus $\Bbb T_L^ν=\Bbb R^ν/L\cdot\Bbb Z^ν$ of size $L$, $ν\ge3$. 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 $ν=2$. The method of that proof was primarily dynamical-geometric, whereas the present approach is inherently algebraic.