Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers
arXiv:math/0207223 · doi:10.1088/0951-7715/17/1/001
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.
24 pages, AMS-TeX file