Automorphisms of $\mathbb C^2$ with an invariant non-recurrent attracting Fatou component biholomorphic to $\mathbb C\times \mathbb C^\ast$

Filippo Bracci (1) , Jasmin Raissy (2) , Berit Stensønes (3)

1 DIPMAT - Dipartimento di Matematica [Roma II]
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 NTNU - Norwegian University of Science and Technology [Trondheim]

We prove the existence of automorphisms of $\mathbb C^2$ having an invariant, non-recurrent Fatou component biholomorphic to $\mathbb C \times \mathbb C^\ast$ which is attracting, in the sense that all the orbits converge to a fixed point on the boundary of the component.

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Filippo Bracci, Jasmin Raissy, Berit Stensønes. Automorphisms of $\mathbb C^2$ with an invariant non-recurrent attracting Fatou component biholomorphic to $\mathbb C\times \mathbb C^\ast$. 2017. ⟨hal-01610350v1⟩