Nandor Simanyi (University of Alabama, Birmingham)

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 $m_1,\dots,m_N$ and radius $r$ in the flat unit torus ${\mathbb{T}}^\nu$ , $\nu\ge2$ . 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 ${\mathbb{T}}^\nu$ ($\nu\ge3$ ), we prove that every such system (is fully hyperbolic and) has open ergodic components.