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Entropy continuity for interval maps with holes

Published online by Cambridge University Press:  24 January 2017

OSCAR F. BANDTLOW  and
HANS HENRIK RUGH
OSCAR F. BANDTLOW
Affiliation:
School of Mathematical Sciences, Queen Mary University of London, London E3 4NS, UK email o.bandtlow@qmul.ac.uk
HANS HENRIK RUGH
Affiliation:
Laboratoire de Mathématiques d’Orsay, Université Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay Cedex, France email hans-henrik.rugh@math.u-psud.fr
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Abstract

We study the dependence of the topological entropy of piecewise monotonic maps with holes under perturbations, for example sliding a hole of fixed size at uniform speed or expanding a hole at a uniform rate. We show that under suitable conditions the topological entropy varies locally Hölder continuously with the local Hölder exponent depending itself on the value of the topological entropy.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 38 , Issue 6 , September 2018 , pp. 2036 - 2061
Copyright
© Cambridge University Press, 2017 

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