2016/10/17 by Mauricio Poletti, Marcelo Viana, Poletti, Mauricio +1 · 1 citation
Mathematics · Physics and Astronomy · #37D25 #37D30 #37H15 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems #math.DS #msc:37D25 #msc:37D30 #msc:37H15
paper · pdf · doi:10.48550/arxiv.1610.05294
To appear in Nonlinearity
openalex publication_date 2016/10/17 · arxiv created 2018/11/06 · arxiv updated 2018/11/07 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
Criteria for the simplicity of the Lyapunov spectra of linear cocycles have been found by Furstenberg, Guivarc'h-Raugi, Gol'dsheid-Margulis and, more recently, Bonatti-Viana and Avila-Viana. In all the cases, the authors consider cocycles over hyperbolic systems, such as shift maps or Axiom A diffeomorphisms. In this paper we propose to extend such criteria to situations where the base map is just partially hyperbolic. This raises several new issues concerning, among others, the recurrence of the holonomy maps and the (lack of) continuity of the Rokhlin disintegrations of u-states. Our main results are stated for certain partially hyperbolic skew-products whose iterates have bounded derivatives along center leaves. They allow us, in particular, to exhibit non-trivial examples of stable simplicity in the partially hyperbolic setting.