Dynamics of asymptotically holomorphic polynomial-like maps
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.06122
- arXiv:
- arXiv:1804.06122
- Bibcode:
- 2018arXiv180406122C
- Keywords:
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- Mathematics - Dynamical Systems
- E-Print:
- 47 pages