On the ergodicity of partially hyperbolic systems

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 $C^{1+\delta}$ partially hyperbolic systems.

Authors

Keith Burns

Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, United States

Amie Wilkinson

Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208-2730, United States