Dynamics of asymptotically holomorphic polynomial-like maps
| Autor: | Clark, Trevor, de Faria, Edson, van Strien, Sebastian |
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| Rok vydání: | 2018 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 47 pages |
| Databáze: | arXiv |
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