Parabolic implosion for endomorphisms of $\mathbb{C}^2$
Complex Variables
2016-07-28 v1 Dynamical Systems
Abstract
We give an estimate of the discontinuity of the large Julia set for a perturbation of a class of maps tangent to the identity, by means of a two-dimensional Lavaurs Theorem. We adapt to our situation a strategy due to Bedford, Smillie and Ueda in the semiattracting setting. We also prove the discontinuity of the filled Julia set for such perturbations of regular polynomials.
Keywords
Cite
@article{arxiv.1607.08104,
title = {Parabolic implosion for endomorphisms of $\mathbb{C}^2$},
author = {Fabrizio Bianchi},
journal= {arXiv preprint arXiv:1607.08104},
year = {2016}
}