SRB Measures for Mostly Expanding Partially Hyperbolic Diffeomorphisms via the Variational Approach

David Burguet; Dawei Yang

doi:10.1093/imrn/rnaf053

SRB Measures for Mostly Expanding Partially Hyperbolic Diffeomorphisms via the Variational Approach

David Burguet
, Dawei Yang

Université de Picardie Jules Verne
Soochow University

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

1 Citation (Scopus)

Abstract

By using the variational approach, we prove the existence of Sinai–Ruelle–Bowen measures for partially hyperbolic C¹ diffeomorphisms with mostly expanding properties. The same conclusion holds true if one considers a dominated splitting E ⊕ F, where dimE = 1 and F is mostly expanding. When the diffeomorphisms are C^1+α, we prove the basin covering property for both cases.

Original language	English
Article number	rnaf053
Journal	International Mathematics Research Notices
Volume	2025
Issue number	6
DOIs	https://doi.org/10.1093/imrn/rnaf053
Publication status	Published - 1 Mar 2025
Externally published	Yes

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title = "SRB Measures for Mostly Expanding Partially Hyperbolic Diffeomorphisms via the Variational Approach",

abstract = "By using the variational approach, we prove the existence of Sinai–Ruelle–Bowen measures for partially hyperbolic C1 diffeomorphisms with mostly expanding properties. The same conclusion holds true if one considers a dominated splitting E ⊕ F, where dimE = 1 and F is mostly expanding. When the diffeomorphisms are C1+α, we prove the basin covering property for both cases.",

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N2 - By using the variational approach, we prove the existence of Sinai–Ruelle–Bowen measures for partially hyperbolic C1 diffeomorphisms with mostly expanding properties. The same conclusion holds true if one considers a dominated splitting E ⊕ F, where dimE = 1 and F is mostly expanding. When the diffeomorphisms are C1+α, we prove the basin covering property for both cases.

AB - By using the variational approach, we prove the existence of Sinai–Ruelle–Bowen measures for partially hyperbolic C1 diffeomorphisms with mostly expanding properties. The same conclusion holds true if one considers a dominated splitting E ⊕ F, where dimE = 1 and F is mostly expanding. When the diffeomorphisms are C1+α, we prove the basin covering property for both cases.

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DO - 10.1093/imrn/rnaf053

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SRB Measures for Mostly Expanding Partially Hyperbolic Diffeomorphisms via the Variational Approach

Abstract

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