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A Note on Permutations and Topological Entropy of Continuous Maps of the Interval

Published online by Cambridge University Press:  20 November 2018

Bill Byers
Bill Byers*
Affiliation:
Concordia UniversityMontreal, Quebec, Canada, H4B 1R6
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Abstract

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Suppose f is a continuous endomorphism of an interval which has a periodic orbit, p0 < P1 < … < pn, that defines a permutation a by f(pi) = pσ(i). If σ is irreducible the topological entropy of f is bounded below by the logarithm of the spectral radius of an n x n matrix which is induced by σ.

Keywords

Primary54H20Secondary58F20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 91 - 95
Copyright
Copyright © Canadian Mathematical Society 1986

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