Links of homeomorphisms of surfaces and topological entropy
type: Item
instance of: scholarly article
title: Links of homeomorphisms of surfaces and topological entropy
zbMATH Open document ID: 0567.58020
author: Tsuyoshi Kobayashi
published in: Proceedings of the Japan Academy. Series A
publication date: 1984-01-01T00:00:00Z
review text: Let f be an orientation preserving self-homeomorphism of a compact surface F with an f-invariant set \(\Sigma\) of finite points in Int F. Let \(M_ f\) be the mapping torus of f. Then \(M_ f\) is a 3-dimensional manifold, and we can naturally construct a link \(L_{f,\Sigma}\) in \(M_ f\) from \(\Sigma\). In this paper, we show that if the topological entropy h(f) of f is equal to zero, then \(L_{f,\Sigma}\) is a graph link. And, conversely, if \(L_{f,\Sigma}\) is a graph link, then f is isotopic rel \(\Sigma\) to a homeomorphism g such that \(h(g)=0\). Moreover, if \(L_{f,\Sigma}\) is not a graph link and f is differentiable at each point of \(\Sigma\), then f has infinitely many periodic orbits whose periods are mutually distinct.
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 3905508
zbMATH Keywords: mapping torus
zbMATH Keywords: topological entropy
zbMATH Keywords: graph link
MaRDI profile type: Publication
full work available at URL: pjaa.60.381
OpenAlex ID: W1978427509
cites work: Q5619504
cites work: Q3891436
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cites work: On the geometry and dynamics of diffeomorphisms of surfaces
DOI: 10.3792/PJAA.60.381
description: scientific article; zbMATH DE number 3905508