The Boltzmann-Sinai Ergodic Hypothesis in Two Dimensions (Without Exceptional Models)

Abstract

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