On the ergodicity of partially hyperbolic systems

Keith Burns, Amie Wilkinson

Type: Article

Publication Date: 2010-03-17

Citations: 214

DOI: https://doi.org/10.4007/annals.2010.171.451

Abstract

Pugh and Shub have conjectured that essential accessibility implies ergodicity for a C 2 , partially hyperbolic, volume-preserving diffeomorphism.We prove this conjecture under a mild center bunching assumption, which is satisfied in particular by all partially hyperbolic systems with 1-dimensional center bundle.We also obtain ergodicity results for C 1Cı partially hyperbolic systems.

Locations

arXiv (Cornell University) - View - PDF
Annals of Mathematics - View - PDF

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