A Complex Gap Lemma
Dynamical Systems
2018-10-08 v1
Abstract
Inspired by the work of Newhouse in one real variable, we introduce a relevant notion of thickness for dynamical Cantor sets of the plane associated to a holomorphic IFS. Our main result is a complex version of Newhouse's Gap Lemma : we show that under some assumptions, if the product t(K)t(L) of the thicknesses of two Cantor sets K and L is larger than 1, then K and L have non empty intersection. Since in addition this thickness varies continuously, this gives a criterion to get a robust intersection between two Cantor sets in the plane.
Keywords
Cite
@article{arxiv.1810.02544,
title = {A Complex Gap Lemma},
author = {Sébastien Biebler},
journal= {arXiv preprint arXiv:1810.02544},
year = {2018}
}