Unconditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

Academic Article

Abstract

  • 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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    Keywords

  • math.DS, math.DS, 37D50, 34D05
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    Authorlist

  • Simanyi N