Nandor Simanyi
The Boltzmann-Sinai Ergodic Hypothesis in Two Dimensions 
(Without Exceptional Models)
(151K, AMS-TeX)

ABSTRACT.  We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,\dots,m_N$ and radius $r$ in the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. In the case $\nu=2$ we prove (the full hyperbolicity and) the ergodicity of such systems for every selection $(m_1,\dots,m_N;r)$ of the external geometric parameters, without exceptional values. In higher dimensions, for hard ball systems in $\Bbb T^\nu$ ($\nu\ge3$), we prove that every such system (is fully hyperbolic and) has open ergodic components.