Polynomial-like dynamics of analytic maps
Dynamical Systems
2025-10-17 v2 Complex Variables
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.
Cite
@article{arxiv.2508.17308,
title = {Polynomial-like dynamics of analytic maps},
author = {Genadi Levin},
journal= {arXiv preprint arXiv:2508.17308},
year = {2025}
}
Comments
The paper has been revised. Now the main results hold for a substantially bigger class of maps, with a partly different proof