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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	299-317
Nombre de pages	19
journal	Fundamenta Mathematicae
Volume	231
Numéro de publication	3
Les DOIs	https://doi.org/10.4064/fm231-3-5
état	Publié - 1 janv. 2015

Accès au document

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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year = "2015",

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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

U2 - 10.4064/fm231-3-5

DO - 10.4064/fm231-3-5

M3 - Article

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SN - 0016-2736

VL - 231

SP - 299

EP - 317

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

IS - 3