A two-dimensional polynomial mapping with a wandering Fatou component

Matthieu Astorg (1) , Xavier Buff (1) , Romain Dujardin (2) , Han Peters (3) , Jasmin Raissy (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
3 Korteweg-de Vries Institute for Mathematics

We show that there exist polynomial endomorphisms of ℂ^2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of P^2(C). We also find real examples with wandering domains in ℝ^2. The proof is based on parabolic implosion techniques, and is based on an original idea of M. Lyubich.

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

Matthieu Astorg, Xavier Buff, Romain Dujardin, Han Peters, Jasmin Raissy. A two-dimensional polynomial mapping with a wandering Fatou component. Annals of Mathematics, 2016, 184 (1), pp.263-313. ⟨10.4007/annals.2016.184.1.2⟩. ⟨hal-01610414⟩