2006/11/25 by Federico Rodriguez Hertz, Hertz, F. Rodriguez, M. A. Rodriguez Hertz +3
Mathematics · Physics and Astronomy · #37A25 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.math/0611787
openalex publication_date 2006/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [15] the authors proved the Pugh-Shub conjecture for partially hyperbolic diffeomorphisms with 1-dimensional center, i.e. stable ergodic diffeomorphism are dense among the partially hyperbolic ones. In this work we address the issue of giving a more accurate description of this abundance of ergodicity. In particular, we give the first examples of manifolds in which all conservative partially hyperbolic diffeomorphisms are ergodic.