- 02-321 Nandor Simanyi
- Proving The Ergodic Hypothesis for Billiards With Disjoint Cylindric Scatterers
Jul 24, 02
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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.