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

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

Résumé

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.

langue originale	Anglais
Pages (de - à)	1485-1510
Nombre de pages	26
journal	Annales Henri Poincare
Volume	25
Numéro de publication	2
Les DOIs	https://doi.org/10.1007/s00023-023-01308-y
état	Publié - 1 févr. 2024

Accès au document

10.1007/s00023-023-01308-y

Autres fichiers et liens

Lien vers la publication dans Scopus

Contient cette citation

@article{c149edd5d25646b18783577d3f5ec526,

title = "Maximal Measure and Entropic Continuity of Lyapunov Exponents for Cr Surface Diffeomorphisms with Large Entropy",

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.",

keywords = "37A35, 37C40, 37D25",

author = "David Burguet",

note = "Publisher Copyright: {\textcopyright} Springer Nature Switzerland AG 2023.",

year = "2024",

month = feb,

day = "1",

doi = "10.1007/s00023-023-01308-y",

language = "English",

volume = "25",

pages = "1485--1510",

journal = "Annales Henri Poincare",

issn = "1424-0637",

number = "2",

}

TY - JOUR

T1 - Maximal Measure and Entropic Continuity of Lyapunov Exponents for Cr Surface Diffeomorphisms with Large Entropy

AU - Burguet, David

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

PY - 2024/2/1

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

U2 - 10.1007/s00023-023-01308-y

DO - 10.1007/s00023-023-01308-y

M3 - Article

AN - SCOPUS:85153043455

SN - 1424-0637

VL - 25

SP - 1485

EP - 1510

JO - Annales Henri Poincare

JF - Annales Henri Poincare

IS - 2