Topological entropy of maps on regular curves
type: Item
instance of: scholarly article
title: Topological entropy of maps on regular curves
zbMATH Open document ID: 1139.37007
author: Hisao Kato
published in: Topology and its Applications
publication date: 2007-03-12T00:00:00Z
review text: It is known that the topological entropy of a homeomorphism on a regular curve is zero, see \textit{G. T. Seidler} [Proc. Am. Math. Soc. 108, No.~4, 1025--1030 (1990; Zbl 0703.54021)]. Here, more generally, the topological entropy of a map \(f\) on a regular curve \(X\) is studied in terms of the growth of the number of components of \(f^{-n}(y), y\in X\). The proof of the main statement uses the boundary bumping theorem from [\textit{S. B. Nadler jun.}, Continuum theory. An introduction, Pure and Applied Mathematics (New York, Marcel Dekker), 158, New York: Marcel (1992; Zbl 0757.54009)].
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 54C70
zbMATH DE Number: 5132965
zbMATH Keywords: growth of the number of components
zbMATH Keywords: boundary bumping theorem
MaRDI profile type: Publication
full work available at URL: j.topol.2006.10.011
OpenAlex ID: W2007117606
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DOI: 10.1016/J.TOPOL.2006.10.011
description: scientific article; zbMATH DE number 5132965