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

Year: 2025

Type: article

Abstract: By using the variational approach, we prove the existence of Sinai–Ruelle–Bowen measures for partially hyperbolic $\mathcal C^{1}$ diffeomorphisms with mostly expanding properties. The same conclusion holds true if one considers a dominated splitting $E\oplus F$, where $\operatorname{dim} E=1$ and $F$ is mostly expanding. When the diffeomorphisms are $\mathcal C^{1+\alpha }$, we prove the basin covering property for both cases.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnaf053

Authors: David Burguet, Dawei Yang

Institutions: Centre National de la Recherche Scientifique, Laboratoire Amiénois de Mathématique Fondamentale et Appliquée, Université de Picardie Jules Verne, Soochow University

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4408461849

FWCI: 1.604

Cites: 26

Cited by: 1

Related to: 10