| Full text | |
| Author(s): |
Clark, Trevor
;
De Faria, Edson
;
Van Strien, Sebastian
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Ergodic Theory and Dynamical Systems; v. N/A, p. 49-pg., 2022-11-29. |
| 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. (AU) | |
| FAPESP's process: | 16/25053-8 - Dynamics and geometry in low dimensions |
| Grantee: | André Salles de Carvalho |
| Support Opportunities: | Research Projects - Thematic Grants |
| FAPESP's process: | 16/25970-0 - Renormalization of asymptotically holomorphic systems |
| Grantee: | Edson de Faria |
| Support Opportunities: | Scholarships abroad - Research |