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arXiv · 2609.03610

Dynamical (non-)recurrence of escaping exponential maps

Weiwei Cui·Jiaxing Huang·Jun Wang
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Abstract

We show that exponential maps could have complicated measurable behaviours by giving two examples in the exponential family both with singular value escaping to infinity ``slowly", one of which is recurrent (in the sense that every positive measure set will return to itself infinitely many times), while the other is non-recurrent. This also complements earlier results of Lyubich, Rees, Urba\'nski-Zdunik, and Hemke. We also give an example of exponential maps with singular value escaping to infinity arbitrarily slow, which is a parametric analog of a result of Rempe.

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Weiwei Cui, Jiaxing Huang, Jun Wang. 2026-09-03. Dynamical (non-)recurrence of escaping exponential maps. https://arxiv.org/abs/2609.03610

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