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arXiv · 2508.17308

Polynomial-like dynamics of analytic maps

Genadi Levin
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Abstract

The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under some natural conditions, a map of this class has a completely invariant compact set if and only if this set is the filled Julia set of a polynomial-like restriction of the map. We also generalize this result to include maps with non-connected domains of definition.

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Genadi Levin. 2025-08-24. Polynomial-like dynamics of analytic maps. https://arxiv.org/abs/2508.17308

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