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

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