**abstract:**
For a holomorphic map \(f : M â†’ M\), 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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