Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

Details Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

2008-03-21

arxiv.org/abs/0803.3112v10

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The paper is withdrawn due to an error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. The present proof does not use the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools from geometric analysis.

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