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arXiv · 2307.16682

Wandering domains with nearly bounded orbits

Leticia Pardo-Simón·David J. Sixsmith
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Abstract

A major open question in transcendental dynamics asks if it is possible for points in a wandering domain to have bounded orbits, and more strongly, for a wandering domain to iterate only in a bounded domain. In this paper we give a partial answer to this question, by constructing a bounded wandering domain that spends, in a precise sense, nearly all of its time iterating in a bounded domain. This is in strong contrast to all previously known examples of wandering domains.

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Leticia Pardo-Simón, David J. Sixsmith. 2023-07-31. Wandering domains with nearly bounded orbits. https://arxiv.org/abs/2307.16682

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