 06158 Nandor Simanyi
 Conditional Proof of the BoltzmannSinai Ergodic Hypothesis (Assuming the Hyperbolicity of Typical Singular Orbits)
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May 14, 06

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Abstract. We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,\dots,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. We prove the so called BoltzmannSinai Ergodic Hypothesis, i. e. the full hyperbolicity and ergodicity of such systems for every selection $(m_1,\dots,m_N;r)$ of the external geometric parameters, under the assumption that almost every singular trajectory is geometrically
hyperbolic (sufficient), i. e. the so called ChernovSinai Ansatz holds
true for the model. The present proof does not use at all the formerly
developed, rather involved algebraic techniques, instead it employs
exclusively dynamical methods and tools from geometric analysis.
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