The Boltzmann--Sinai Ergodic Hypothesis In Full Generality

Details The Boltzmann--Sinai Ergodic Hypothesis In Full Generality The Boltzmann--Sinai Ergodic Hypothesis In Full Generality

2010-07-07

arxiv.org/abs/1007.1206v2

Mathematics

Dynamical Systems

19 pages, the definition of convex hypersurfaces has been changed (at the beginning of Section 2), and the proof of Propositio

Scientific paper

In the ergodic theory of semi-dispersing billiards the Local Ergodic Theorem, proved by Chernov and Sinai in 1987, plays a central role. So far, all existing proofs of this theorem had to use an annoying global hypothesis, namely the almost sure hyperbolicity of singular orbits. (This is the so called Chernov--Sinai Ansatz.) Here we introduce some new geometric ideas to overcome this difficulty and liberate the proof from the tyranny of the Ansatz. The presented proof is a substantial generalization of my previous joint result with N. Chernov (which is a $2D$ result) to arbitrary dimensions. An important corollary of the presented ansatz-free proof of the Local Ergodic Theorem is finally completing the proof of the Boltzmann--Sinai Ergodic Hypothesis for hard ball systems in full generality.

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