2019/12/17 by Changguang Dong, Dong, Changguang, Adam Kanigowski +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.1912.08132
openalex publication_date 2019/12/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the Bernoulli property for a class of partially hyperbolic systems arising from skew products. More precisely, we consider a hyperbolic map (T,M,μ), where μ is a Gibbs measure, an aperiodic Hölder continuous cocycle ϕ:M→ \mathbb R with zero mean and a zero-entropy flow (Kt,N,ν). We then study the skew product Tϕ(x,y)=(Tx,Kϕ(x)y), acting on (M× N,μ× ν). We show that if (Kt) is of slow growth and has good equidistribution properties, then Tϕ remains Bernoulli. In particular, our main result applies to (Kt) being a typical translation flow on a surface of genus ≥ 1 or a smooth reparametrization of isometric flows on \mathbb T2. This provides examples of non-algebraic, partially hyperbolic systems which are Bernoulli and for which the center is non-isometric (in fact might be weakly mixing).