Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards

Details Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards

2007-05-29

arxiv.org/abs/0705.4125v3

J. Stat. Phys. Vol. 139. No. 3 (2010), 355-366

Mathematics

Dynamical Systems

17 pages, 2 figures

Scientific paper

10.1007/s10955-010-9927-6

The Local Ergodic Theorem (also known as the `Fundamental Theorem') gives sufficient conditions under which a phase point has an open neighborhood that belongs (mod 0) to one ergodic component. This theorem is a key ingredient of many proofs of ergodicity for billiards and, more generally, for smooth hyperbolic maps with singularities. However the proof of that theorem relies upon a delicate assumption (Chernov-Sinai Ansatz), which is difficult to check for some physically relevant models, including gases of hard balls. Here we give a proof of the Local Ergodic Theorem for two dimensional billiards without using the Ansatz.

Affiliated with

Also associated with

No associations

Rating

Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards 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 Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Upgrading the Local Ergodic Theorem for planar semi-dispersing billiards will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-498881