Links of homeomorphisms of a disk and topological entropy
type: Item
instance of: scholarly article
title: Links of homeomorphisms of a disk and topological entropy
zbMATH Open document ID: 0585.57005
DOI: 10.1007/BF01388553
author: Tsuyoshi Kobayashi
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143224
review text: For f an orientation preserving homeomorphism of a disc \({\mathbb{D}}^ 2\) with a finite f-invariant set \(\Sigma =\{p_ 1,...,p_ n\}\) of periodic points in int \({\mathbb{D}}^ 2\) a condition which implies chaos (positive entropy) is found. This condition concerns the link given by the simple closed curves of the suspension (\(\Sigma\),f) in the solid torus - the suspension \(({\mathbb{D}}^ 2,f)\) (more exactly the link in \(S^ 3\), the equator of the complementary solid torus added). In other words the condition concerns an isotopy class of \(Diff({\mathbb{D}}^ 2,\Sigma)\) to which a diffeomorphism isotopic to f belongs. The theory of 3-manifolds and pseudo-Anosov homeomorphisms is used.
Mathematics Subject Classification ID: 57N05
Mathematics Subject Classification ID: 37B99
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57N10
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 3938047
zbMATH Keywords: orientation preserving homeomorphism of a disc
zbMATH Keywords: periodic points
zbMATH Keywords: chaos
zbMATH Keywords: positive entropy
zbMATH Keywords: suspension
zbMATH Keywords: link in \(S^ 3\)
zbMATH Keywords: pseudo-Anosov homeomorphisms
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3938047