Accessibility and stable ergodicity for partially hyperbolic diffeomorphisms with 1d-center bundle

2006/10/30 by Rodriguez-Hertz, F., Rodriguez-Hertz, M., Ures, R. · 3 citations
#Dynamical Systems (math.DS) #FOS: Mathematics #Primary 37D30 #Secondary 37A25

paper · doi:10.48550/arxiv.math/0610864

Abstract

We prove that stable ergodicity is C r open and dense among conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle, for all r in [2,infty]. The proof follows Pugh-Shub program: among conservative partially hyperbolic diffeomorphisms with one-dimensional center bundle, accessibility is C r open and dense, and essential accessibility implies ergodicity.

Cited by

• Characterization of Ergodic Measures of Maximal Entropy for Topologically Transitive Partially Hyperbolic Diffeomorphisms with compact center leaves
• Simple Lyapunov spectrum of partially hyperbolic diffeomorphisms
• Partially hyperbolic diffeomorphisms homotopic to the identity in dimension three

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