Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers
Dynamical Systems
2010-08-12 v3 Mathematical Physics
math.MP
Abstract
In this paper we study the ergodic properties of mathematical billiards describing the uniform motion of a point in a flat torus from which finitely many, pairwise disjoint, tubular neighborhoods of translated subtori (the so called cylindric scatterers) have been removed. We prove that every such system is ergodic (actually, a Bernoulli flow), unless a simple geometric obstacle for the ergodicity is present.
Cite
@article{arxiv.math/0207223,
title = {Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers},
author = {Nandor Simanyi},
journal= {arXiv preprint arXiv:math/0207223},
year = {2010}
}
Comments
24 pages, AMS-TeX file