Inventiones mathematicae

, Volume 177, Issue 2, pp 381–413

Conditional proof of the Boltzmann-Sinai ergodic hypothesis


DOI: 10.1007/s00222-009-0182-x

Cite this article as:
Simányi, N. Invent. math. (2009) 177: 381. doi:10.1007/s00222-009-0182-x


We consider the system of N (≥ 2) elastically colliding hard balls of masses m1,…,mN 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 (m1,…,mN;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)


Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA