Introduction to Fatou components in holomorphic dynamics
Dynamical Systems
2023-02-07 v1 Complex Variables
Abstract
This survey is an introduction to the classification of Fatou components in holomorphic dynamics. We start with the description of the Fatou and Julia sets for rational maps of the Riemann sphere, and finish with an account of the recent results on Fatou components for polynomial skew-products in complex dimension two, where we focus on the key steps in the construction giving the existence of a wandering domain for a polynomial endomorphism of .
Keywords
Cite
@article{arxiv.2302.02669,
title = {Introduction to Fatou components in holomorphic dynamics},
author = {Xavier Buff and Jasmin Raissy},
journal= {arXiv preprint arXiv:2302.02669},
year = {2023}
}
Comments
This work is part of the C.I.M.E. Lecture Notes "Modern Aspects of Dynamical Systems'' to be published in the Springer Lecture Notes in Mathematics -- C.I.M.E. subseries, corresponding to the course taught by the second author in Cetraro in August 2021