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- W3173604188 abstract "We study the Bernoulli property for a class of partially hyperbolic systems arising from skew products. More precisely, we consider a hyperbolic map $(T,M,mu )$, where $mu$ is a Gibbs measure, an aperiodic Hölder continuous cocycle $phi :Mto mathbb {R}$ with zero mean and a zero-entropy flow $(K_t,N,nu )$. We then study the skew product begin{equation*} T_phi (x,y)=(Tx,K_{phi (x)}y), end{equation*} acting on $(Mtimes N,mu times nu )$. We show that if $(K_t)$ is of slow growth and has good equidistribution properties, then $T_phi$ remains Bernoulli. In particular, our main result applies to $(K_t)$ being a typical translation flow on a surface of genus $geq 1$ or a smooth reparametrization of isometric flows on $mathbb {T}^2$. 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)." @default.
- W3173604188 created "2021-07-05" @default.
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- W3173604188 date "2021-06-18" @default.
- W3173604188 modified "2023-10-18" @default.
- W3173604188 title "Bernoulli property for certain skew products over hyperbolic systems" @default.
- W3173604188 doi "https://doi.org/10.1090/tran/8486" @default.
- W3173604188 hasPublicationYear "2021" @default.
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