Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

Abstract

We consider the system of $N$ ($\ge 2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus ${\mathbb{T}}^{\nu }$, $\nu \ge 2$. 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 geometric 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.

Final version; to appear in Inventiones Mathematicae

References in corpus (2)

• Proof of the Ergodic Hypothesis for Typical Hard Ball Systems
• Flow-invariant hypersurfaces in semi-dispersing billiards

Cited by in corpus (4)

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• Stable regimes for hard disks in a channel with twisting walls