CRM: Centro De Giorgi
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KAWA - Komplex Analysis Workshop VI, 2015

A polynomial endomorphism of \(\mathbb{C}^2\) with a wandering Fatou component

speaker: Matthieu Astorg ( Université Paul Sabatier of Toulouse, France)

abstract: For a holomorphic map \(f : M → M\), where \(M\) is a complex manifold, the Fatou set is the largest open set on which the iterates of f form a normal family, and a Fatou component is a connected component of the Fatou set. A celebrated theorem of Sullivan (1985) asserts that all Fatou component are eventually periodic when \(f\) is a rational map and \(M = P^1(\mathbb{C})\). Various classes of counter-examples have been found and studied when \(M = \mathbb{C}\) and \(f\) is an entire transcendental function. We give a construction for a counterexample in dimension 2, with \(M = P^2(\mathbb{C})\), and \(f\) a polynomial skew-product, using techniques of parabolic implosion. Joint work with X. Buff, R. Dujardin, H. Peters and J. Raissy

Fri 27 Mar, 17:20 - 18:00, Aula Dini
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