On topological entropy of billiard tables with small inner scatterers
type: Item
instance of: scholarly article
title: On topological entropy of billiard tables with small inner scatterers
zbMATH Open document ID: 1230.37020
author: Yi-Chiuan Chen
published in: Advances in Mathematics
publication date: 2010-05-10T00:00:00Z
review text: The author studies the topological entropy of a class of billiard systems, which consists of strictly convex domain in the plane and strictly convex inner scatters. The author proves that the topological entropy of the first return map to the scatters can be made arbitrarily large provided the inner scatters are sufficiently small. The author uses the concept of anti-integrable limits with the theory of Lyusternik-Shnirel'man. These results generalize C. Foltin's result which states that ``there is an open and dense subset of the billiard space with \(K\geq 1\) (the number of convex scatters) in which every billiard flow has positive topological entropy provided the inner scatters are small enough''.
reviewed by: K. Ali Akbar
Mathematics Subject Classification ID: 37B10
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 37C35
Mathematics Subject Classification ID: 37D50
zbMATH DE Number: 5706195
zbMATH Keywords: topological entropy
zbMATH Keywords: anti-integrable limit
zbMATH Keywords: billiards
MaRDI profile type: Publication
full work available at URL: j.aim.2009.11.012
OpenAlex ID: W1987196995
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DOI: 10.1016/J.AIM.2009.11.012
description: scientific article; zbMATH DE number 5706195