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Title: Ergodicity of the generalized lemon billiards

In this paper, we study a two-parameter family of convex billiard tables, by taking the intersection of two round disks (with different radii) in the plane. These tables give a generalization of the one-parameter family of lemon-shaped billiards. Initially, there is only one ergodic table among all lemon tables. In our generalized family, we observe numerically the prevalence of ergodicity among the some perturbations of that table. Moreover, numerical estimates of the mixing rate of the billiard dynamics on some ergodic tables are also provided.
Authors:
 [1] ; ; ;  [2]
  1. Department of Computer Science, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801-2302 (United States)
  2. Department of Mathematics and Statistics, UMass Amherst, Amherst, Massachusetts 01003 (United States)
Publication Date:
OSTI Identifier:
22250944
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 23; Journal Issue: 4; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BIFURCATION; CHAOS THEORY; ORBITS; OZONE; PERTURBATION THEORY