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.
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