Jumps of entropy for Cr interval maps

David Burguet

doi:10.4064/fm231-3-5

Jumps of entropy for C^r interval maps

David Burguet

École Polytechnique

Research output: Contribution to journal › Article › peer-review

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 ⊂ C^r([0,1]) with h_top(f) 蠑 log⁺ ¶f₁¶∞/r . To this end we study the continuity of the entropy of the Buzzi{Hofbauer diagrams associated to Cr interval maps.

Original language	English
Pages (from-to)	299-317
Number of pages	19
Journal	Fundamenta Mathematicae
Volume	231
Issue number	3
DOIs	https://doi.org/10.4064/fm231-3-5
Publication status	Published - 1 Jan 2015

Keywords

Buzzi-Hofbauer diagram
Entropy
Smooth interval maps

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10.4064/fm231-3-5

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title = "Jumps of entropy for Cr interval maps",

abstract = "We study the jumps of topological entropy for Cr interval or circle maps. We prove in particular that the topological entropy is continuous at any f ⊂ Cr([0,1]) with htop(f) 蠑 log+ ¶f1¶∞/r . To this end we study the continuity of the entropy of the Buzzi\{Hofbauer diagrams associated to Cr interval maps.",

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N2 - We study the jumps of topological entropy for Cr interval or circle maps. We prove in particular that the topological entropy is continuous at any f ⊂ Cr([0,1]) with htop(f) 蠑 log+ ¶f1¶∞/r . To this end we study the continuity of the entropy of the Buzzi{Hofbauer diagrams associated to Cr interval maps.

AB - We study the jumps of topological entropy for Cr interval or circle maps. We prove in particular that the topological entropy is continuous at any f ⊂ Cr([0,1]) with htop(f) 蠑 log+ ¶f1¶∞/r . To this end we study the continuity of the entropy of the Buzzi{Hofbauer diagrams associated to Cr interval maps.

KW - Buzzi-Hofbauer diagram

KW - Entropy

KW - Smooth interval maps

UR - https://www.scopus.com/pages/publications/84941557990

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DO - 10.4064/fm231-3-5

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JF - Fundamenta Mathematicae

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Jumps of entropy for C^r interval maps

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