Chapitre D'ouvrage Année : 2024

Introduction to Fatou Components in Holomorphic Dynamics

Résumé

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 updated 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 $\mathbb{C}^2$ .

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Dates et versions

hal-03974841 , version 1 (06-02-2023)

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Xavier Buff, Jasmin Raissy. Introduction to Fatou Components in Holomorphic Dynamics. Modern Aspects of Dynamical Systems, 2347, Springer Nature Switzerland, pp.59-103, 2024, Lecture Notes in Mathematics, ⟨10.1007/978-3-031-62014-0_2⟩. ⟨hal-03974841⟩
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