Work

Abundance of stable ergodicity

Year: 2004

Type: article

Abstract: We consider the set \mathcal{PH}_\omega(M) of volume preserving partially hyperbolic diffeomorphisms on a compact manifold having 1-dimensional center bundle. We show that the volume measure is ergodic, and even Bernoulli, for any C^2 diffeomorphism in an open and dense subset of \mathcal{PH}_\omega(M) . This solves a conjecture of Pugh and Shub, in this setting.

Source: Commentarii Mathematici Helvetici

DOI: 10.1007/s00014-004-0819-8

Authors: Christian Bonatti, Carlos Matheus, Marcelo Viana, Amie Wilkinson

Institutions: Université de Bourgogne, Instituto Nacional de Matemática Pura e Aplicada, Université Sorbonne Paris Nord, Northwestern University, University of Chicago

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Université de Bourgogne

Award: Ergodic and Geometric Properties of Diffeomorphisms