Maximal Measure and Entropic Continuity of Lyapunov Exponents for Cr Surface Diffeomorphisms with Large Entropy

David Burguet

doi:10.1007/s00023-023-01308-y

Maximal Measure and Entropic Continuity of Lyapunov Exponents for C^r Surface Diffeomorphisms with Large Entropy

David Burguet

École Polytechnique

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

Abstract

We prove a finite smooth version of the entropic continuity of Lyapunov exponents proved recently by Buzzi, Crovisier, and Sarig for C^∞ surface diffeomorphisms (Buzzi et al., Invent Math 230(2):767–849, 2022). As a consequence, we show that any C^r, r>1, smooth surface diffeomorphism f with h_top(f)>1rlim sup_n1nlog⁺‖dfn‖_∞ admits a measure of maximal entropy. We also prove the C^r continuity of the topological entropy at f.

Original language	English
Pages (from-to)	1485-1510
Number of pages	26
Journal	Annales Henri Poincare
Volume	25
Issue number	2
DOIs	https://doi.org/10.1007/s00023-023-01308-y
Publication status	Published - 1 Feb 2024

Keywords

37A35
37C40
37D25

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10.1007/s00023-023-01308-y

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abstract = "We prove a finite smooth version of the entropic continuity of Lyapunov exponents proved recently by Buzzi, Crovisier, and Sarig for C∞ surface diffeomorphisms (Buzzi et al., Invent Math 230(2):767–849, 2022). As a consequence, we show that any Cr, r>1, smooth surface diffeomorphism f with htop(f)>1rlim supn1nlog+‖dfn‖∞ admits a measure of maximal entropy. We also prove the Cr continuity of the topological entropy at f.",

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AU - Burguet, David

N1 - Publisher Copyright: © Springer Nature Switzerland AG 2023.

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Y1 - 2024/2/1

N2 - We prove a finite smooth version of the entropic continuity of Lyapunov exponents proved recently by Buzzi, Crovisier, and Sarig for C∞ surface diffeomorphisms (Buzzi et al., Invent Math 230(2):767–849, 2022). As a consequence, we show that any Cr, r>1, smooth surface diffeomorphism f with htop(f)>1rlim supn1nlog+‖dfn‖∞ admits a measure of maximal entropy. We also prove the Cr continuity of the topological entropy at f.

AB - We prove a finite smooth version of the entropic continuity of Lyapunov exponents proved recently by Buzzi, Crovisier, and Sarig for C∞ surface diffeomorphisms (Buzzi et al., Invent Math 230(2):767–849, 2022). As a consequence, we show that any Cr, r>1, smooth surface diffeomorphism f with htop(f)>1rlim supn1nlog+‖dfn‖∞ admits a measure of maximal entropy. We also prove the Cr continuity of the topological entropy at f.

KW - 37A35

KW - 37C40

KW - 37D25

UR - https://www.scopus.com/pages/publications/85153043455

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JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 2

ER -

Maximal Measure and Entropic Continuity of Lyapunov Exponents for C^r Surface Diffeomorphisms with Large Entropy

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Keywords

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