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arXiv · 1804.06122

Dynamics of asymptotically holomorphic polynomial-like maps

Trevor Clark·Edson de Faria·Sebastian van Strien
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Abstract

The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of asymptotically holomorphic extensions of $C^r$ ($r>3$) unimodal maps that are infinitely renormalizable of bounded type. Here we prove a version of the Fatou-Julia-Sullivan theorem and a topological straightening theorem in this setting. In particular, these maps do not have wandering domains and their Julia sets are locally connected.

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Trevor Clark, Edson de Faria, Sebastian van Strien. 2018-04-17. Dynamics of asymptotically holomorphic polynomial-like maps. https://arxiv.org/abs/1804.06122

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