Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers

Details Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers

2002-07-24

arxiv.org/abs/math/0207223v3

Nonlinearity, volume 17 (2004), pp. 1 - 21

Mathematics

Dynamical Systems

24 pages, AMS-TeX file

Scientific paper

10.1088/0951-7715/17/1/001

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.

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