English

A two-dimensional polynomial mapping with a wandering Fatou component

Dynamical Systems 2014-12-10 v2 Complex Variables

Abstract

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.

Keywords

Cite

@article{arxiv.1411.1188,
  title  = {A two-dimensional polynomial mapping with a wandering Fatou component},
  author = {Matthieu Astorg and Xavier Buff and Romain Dujardin and Han Peters and Jasmin Raissy},
  journal= {arXiv preprint arXiv:1411.1188},
  year   = {2014}
}

Comments

Revised introduction

R2 v1 2026-06-22T06:48:41.514Z