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arXiv · 2610.26018

Bernoulli property for skew products of exponentially mixing systems over Anosov bases

Changguang Dong·Qiujie Qiao
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Abstract

We study $C^{1+β}$ skew products over topologically mixing Anosov diffeomorphisms, with fiber dynamics generated by a locally free $\mathbb{R}^k$-action. For a Gibbs measure on the base and a cocycle with a nonzero average, we establish a Bernoulli criterion for ergodic invariant product measures. The fiber hypotheses apply to actions that are exponentially mixing with respect to the SRB measure, as well as volume measures that are almost exponentially mixing with a limit SRB measure. As an application, when the fibers are generated by geodesic flows or Weyl chamber actions, our results reveal a statistical phase transition determined by the drift.

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Changguang Dong, Qiujie Qiao. 2026-10-19. Bernoulli property for skew products of exponentially mixing systems over Anosov bases. https://arxiv.org/abs/2610.26018

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