The Boltzmann-Sinai Ergodic Hypothesis in Two Dimensions (Without Exceptional Models)

2004/07/22 by Simanyi, Nandor
#34D05 #37D50 #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.math/0407368

Abstract

We consider the system of N (≥2) elastically colliding hard balls of masses m₁,...,m_N and radius r in the flat unit torus \Bbb T^ν, ν≥2. In the case ν=2 we prove (the full hyperbolicity and) the ergodicity of such systems for every selection (m₁,...,m_N;r) of the external geometric parameters, without exceptional values. In higher dimensions, for hard ball systems in \Bbb T^ν (ν≥3), we prove that every such system (is fully hyperbolic and) has open ergodic components.

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