Irregular sets for a class of skew product transformations

Nian Liu; Xue Liu

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arXiv · 2404.12562

Irregular sets for a class of skew product transformations

Nian Liu·Xue Liu

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Abstract

In this paper, we study the irregular set of any continuous observable for a class of skew product transformations, which is driven by a uniquely ergodic homeomorphism system $(\Omega,\mathbb{P},\theta)$ and satisfies Anosov and toplogical mixing on fibers property. We prove that if the irregular set of any continuous observable is nonempty on a fiber, then the irregular set must be nonempty, residual, and carry full fiber topological entropy on $\mathbb{P}$-a.e. fibers. The orbit-gluing technique provided by the fiber specification property are utilized.

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Nian Liu, Xue Liu. 2024-04-19. Irregular sets for a class of skew product transformations. https://arxiv.org/abs/2404.12562

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