Inventiones mathematicae

, Volume 177, Issue 2, pp 381-413

Conditional proof of the Boltzmann-Sinai ergodic hypothesis

  • Nándor SimányiAffiliated withDepartment of Mathematics, University of Alabama at Birmingham Email author 

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We consider the system of N (≥ 2) elastically colliding hard balls of masses m 1,…,m N and radius r on the flat unit torus \(\mathbb{T}^{\nu}\) , ν≥2. 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 parameters, provided that almost every singular orbit is geometrically hyperbolic (sufficient), i.e. the so called Chernov-Sinai Ansatz is true. The present proof does not use the formerly developed, rather involved algebraic techniques, instead it employs exclusively dynamical methods and tools from geometric analysis.

Mathematics Subject Classification (2000)

37D50 34D05