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On the topological entropy of transitive maps of the interval

Published online by Cambridge University Press:  17 April 2009

Ethan M. Coven  and
Melissa C. Hidalgo
Ethan M. Coven
Affiliation:
Department of Mathematics, Wesleyan University, Middletown, CT 06457, United States of America
Melissa C. Hidalgo
Affiliation:
Department of Mathematics, University of Hartford, West Hartford, CT 06117, United States of America
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Abstract

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The topological entropy of a continuous map of the interval is the supremum of the topological entropies of the piecewise linear maps associated to its finite invariant sets. We show that for transitive maps, this supremum is attained at some finite invariant set if and only if the map is piecewise monotone and the set contains the endpoints of the interval and the turning points of the map.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 2 , October 1991 , pp. 207 - 213
Copyright
Copyright © Australian Mathematical Society 1991

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