no. 6
SRB measures for higher dimensional singular partially hyperbolic attractors
[Mesures SRB pour des attracteurs partiellement hyperboliques avec singularité(s) en dimension finie quelconque]
Leplaideur, Renaud1 ; Yang, Dawei2
1 LMBA, UMR6205 Université de Brest 6, avenue Victor Le Gorgeu C.S. 93837, France
2 School of Mathematical Sciences, Soochow University, No. 1, Shizi Street, Suzhou, 215006, P.R. China
Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2703-2717.

Nous prouvons que tout attracteur partiellement hyperbolique de dimension finie et avec singularité(s) admet une unique mesure SRB. La preuve utilise des outils simples et généraux du formalisme thermodynamique et ne nécessite pas de recourir à une section de Poincaré.

We prove the existence and the uniqueness of the SRB measure for any singular hyperbolic attractor in dimension d≥3. The proof does not use Poincaré sectional maps, but uses basic properties of thermodynamical formalism.

Reçu le :
Révisé le :
Accepté le :
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DOI : 10.5802/aif.3148
Classification : 37A35, 37A60, 37D20, 37D35, 47N10
Keywords: partially hyperbolic singular flows, thermodynamical formalism, equilibrium states, SRB and physical measures
Mot clés : flots partiellement hyperboliques, formalisme thermodynamique, état d’équilibre, mesures SRB et physiques
Leplaideur, Renaud 1 ; Yang, Dawei 2

1 LMBA, UMR6205 Université de Brest 6, avenue Victor Le Gorgeu C.S. 93837, France
2 School of Mathematical Sciences, Soochow University, No. 1, Shizi Street, Suzhou, 215006, P.R. China 
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Leplaideur, Renaud; Yang, Dawei. SRB measures for higher dimensional singular partially hyperbolic attractors. Annales de l'Institut Fourier, Tome 67 (2017) no. 6, pp. 2703-2717. doi : 10.5802/aif.3148. http://www.numdam.org/articles/10.5802/aif.3148/

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