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

Abstract

We consider the system of $N$ ($\ge 2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ in the flat unit torus ${\mathbb{T}}^{\nu }$, $\nu \ge 2$. In the case $\nu =2$ 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 ${\mathbb{T}}^{\nu }$ ($\nu \ge 3$), we prove that every such system (is fully hyperbolic and) has open ergodic components.

Paper withdrawn due to a substantial error

References in corpus (1)

• Proof of the Boltzmann-Sinai Ergodic Hypothesis for Typical Hard Disk Systems

Cited by in corpus (1)

• Deterministic Diffusion in Periodic Billiard Models