Fatou's web
Dynamical Systems
2015-10-27 v1 Complex Variables
Abstract
Let be Fatou's function, that is, . We prove that the escaping set of has the structure of a `spider's web' and we show that this result implies that the non-escaping endpoints of the Julia set of together with infinity form a totally disconnected set. We also give a well-known transcendental entire function, due to Bergweiler, for which the escaping set is a spider's web and we point out that the same property holds for families of functions.
Keywords
Cite
@article{arxiv.1510.07449,
title = {Fatou's web},
author = {Vasiliki Evdoridou},
journal= {arXiv preprint arXiv:1510.07449},
year = {2015}
}