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Jumps of entropy for $C^r$ interval maps

Volume 231 / 2015

David Burguet Fundamenta Mathematicae 231 (2015), 299-317 MSC: 37A35, 37C05, 37B10, 37B40. DOI: 10.4064/fm231-3-5

Abstract

We study the jumps of topological entropy for $C^r$ interval or circle maps. We prove in particular that the topological entropy is continuous at any $f\in C^r([0,1])$ with $h_{\rm top}(f)>\frac{\log^+\|f'\|_\infty}{r}$. To this end we study the continuity of the entropy of the Buzzi–Hofbauer diagrams associated to $C^r$ interval maps.

Authors

  • David BurguetLPMA – CNRS UMR 7599
    Université Paris 6
    75252 Paris Cedex 05, France
    e-mail

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