Smooth Stable Foliations of Anosov Diffeomorphisms

Ruihao Gu

doi:10.5802/crmath.679

Article de recherche - Systèmes dynamiques

Smooth Stable Foliations of Anosov Diffeomorphisms
[Foliations stables et lisses des difféomorphismes d’Anosov]

Ruihao Gu ¹

¹ Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, Peoples Republic of China

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1763-1771.

Résumé
Abstract

Dans cet article, nous nous concentrons sur la rigidité des foliations stables de codimension un des difféomorphismes d’Anosov en $C^{2 +}$ . Plus précisément, nous montrons que si la régularité de ces foliations est légèrement supérieure à 2, alors elles auront la même régularité que les difféomorphismes.

In this paper, we focus on the rigidity of $C^{2 +}$ -smooth codimension-one stable foliations of Anosov diffeomorphisms. Specifically, we show that if the regularity of these foliations is slightly bigger than 2, then they will have the same smoothness of the diffeomorphisms.

Reçu le : 2023-10-30
Révisé le : 2024-07-10
Accepté le : 2024-08-18
Publié le : 2024-11-25

DOI : 10.5802/crmath.679

Classification : 37C05, 37C15, 37D20
Keywords: Anosov diffeomorphism, stable foliation, rigidity
Mots-clés : difféomorphisme d’Anosov, foliation stables, rigidité

Affiliations des auteurs :

Ruihao Gu ¹

¹ Shanghai Center for Mathematical Sciences, Fudan University, Shanghai 200433, Peoples Republic of China

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Smooth {Stable} {Foliations} of {Anosov} {Diffeomorphisms}},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1763--1771},
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     year = {2024},
     doi = {10.5802/crmath.679},
     language = {en},
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Ruihao Gu. Smooth Stable Foliations of Anosov Diffeomorphisms. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 1763-1771. doi : 10.5802/crmath.679. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.679/

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