Calculating topological entropy
type: Item
instance of: scholarly article
title: Calculating topological entropy
zbMATH Open document ID: 0962.37004
DOI: 10.1007/BF02764219
author: Stewart Baldwin
author: Edward E. Slaminka
published in: Journal of Statistical Physics
publication date: 2000-07-19T00:00:00Z
review text: This paper deals with the attempt to find effective algorithms for calculating the topological entropy of piecewise monotone maps of the interval having more than three pieces. The original motivation for the algorithms described in this paper is based on the following fact: If \(g\) is a piecewise monotone continuous function on the unit interval, then \(h(g)= \lim_{n\to \infty} \frac 1n \log \operatorname {Var}(g^n)\), where \(h(g)\) denotes the topological entropy of \(g\), and Var denotes the total variation. The authors present a modified algorithm based on the above mentioned result and prove that this algorithm is equivalent to the standard power method for finding eigenvalues of matrices (with shift of origin) in those cases for which the function is Markov. The authors present the numerical results when this algorithm is applied to a number of examples.
Mathematics Subject Classification ID: 37B40
Mathematics Subject Classification ID: 37E30
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 65P99
zbMATH DE Number: 1279504
zbMATH Keywords: topological entropy
zbMATH Keywords: piecewise monotone function
zbMATH Keywords: eigenvalues
zbMATH Keywords: Markov function
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1279504