Mathematics – Dynamical Systems
Scientific paper
2004-07-22
Mathematics
Dynamical Systems
Paper withdrawn due to a substantial error
Scientific paper
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 $\Bbb T^\nu$, $\nu\ge2$. 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 $\Bbb T^\nu$ ($\nu\ge3$), we prove that every such system (is fully hyperbolic and) has open ergodic components.
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