Nandor Simanyi
Proof of the Ergodic Hypothesis for Typical Hard Ball Systems
(142K, AMS-TeX)

ABSTRACT.  We consider the system of $N$ ($\ge2$) hard balls with masses $m_1,\dots,m_N$ 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 $(m_1,\dots,m_N;\,L)$ 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.