Dynamics of post-critically finite maps in higher dimension
Dynamical Systems
2016-09-12 v1
Abstract
We study the dynamics of post-critically finite endomorphisms of P^k(C). We prove that post-critically finite endomorphisms are always post-critically finite all the way down under a mild regularity condition on the post-critical set. We study the eigenvalues of periodic points of post-critically finite endomorphisms. Then, under a weak transversality condition and assuming Kobayashi hyperbolicity of the complement of the post-critical set, we prove that the only possible Fatou components are super-attracting basins, thus partially extending to any dimension a result of Fornaess-Sibony and Rong holding in the case k = 2.
Keywords
Cite
@article{arxiv.1609.02717,
title = {Dynamics of post-critically finite maps in higher dimension},
author = {Matthieu Astorg},
journal= {arXiv preprint arXiv:1609.02717},
year = {2016}
}