2012/12/16 by Javier Solano, Solano, Javier
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Stochastic processes and statistical mechanics #math.DS
paper · pdf · doi:10.48550/arxiv.1212.3820
24 pages
arxiv created 2012/12/16 · openalex publication_date 2012/12/16 · arxiv updated 2012/12/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that for certain partially hyperbolic skew-products, non-uniform hyperbolicity along the leaves implies existence of a finite number of ergodic absolutely continuous invariant probability measures which describe the asymptotics of almost every point. The main technical tool is an extension for sequences of maps of a result of de Melo and van Strien relating hyperbolicity to recurrence properties of orbits. As a consequence of our main result, we also obtain a partial extension of Keller's theorem guaranteeing the existence of absolutely continuous invariant measures for non-uniformly hyperbolic one dimensional maps.