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arXiv · 2312.01390

A Chung-Fuchs type theorem for skew product dynamical systems

Xiong Jin
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Abstract

We prove a Chung-Fuchs type theorem for skew product dynamical systems such that for a measurable function on such a system, if its Birkhoff average converges to zero almost surely, and on typical fibres its Birkhoff sums have a non-trivial independent structure, then its associated generalised random walk oscillates, that is the supremum of the random walk equals to $+\infty$ and the infimum equals to $-\infty$.

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Xiong Jin. 2023-12-03. A Chung-Fuchs type theorem for skew product dynamical systems. https://arxiv.org/abs/2312.01390

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