The Boltzmann-Sinai Ergodic Hypothesis in Full Generality (Without Exceptional Models)

Details The Boltzmann-Sinai Ergodic Hypothesis in Full Generality (Without Exceptional Models) The Boltzmann-Sinai Ergodic Hypothesis in Full Generality (Without Exceptional Models)

2005-10-02

arxiv.org/abs/math/0510022v3

Mathematics

Dynamical Systems

The paper is withdrawn due to an error

Scientific paper

We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. We prove the so called Boltzmann-Sinai Ergodic Hypothesis, i. e. the full hyperbolicity and ergodicity of such systems for every selection $(m_1,...,m_N;r)$ of the external geometric parameters, without exceptional values. The present proof does not use at all the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools of geometric analysis.

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