Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

Details Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis

2006-05-14

arxiv.org/abs/math/0605358v6

Inventiones Mathematicae, Vol. 177, No. 2 (2009), pp. 381-413

Mathematics

Dynamical Systems

Final version; to appear in Inventiones Mathematicae

Scientific paper

10.1007/s00222-009-0182-x

We consider the system of $N$ ($\ge2$) elastically colliding hard balls of masses $m_1,...,m_N$ and radius $r$ on the flat unit torus $\Bbb T^\nu$, $\nu\ge2$. 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.

Affiliated with

Also associated with

No associations

Rating

Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Conditional Proof of the Boltzmann-Sinai Ergodic Hypothesis will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-264731