Scale Recurrence Lemma and Dimension Formula for Cantor Sets in the Complex Plane
Dynamical Systems
2024-11-20 v1
Abstract
We will prove a multidimensional conformal version of the scale recurrence lemma of Moreira and Yoccoz \cite{MY} for Cantor sets in the complex plane. We then use this new recurrence lemma, together with the ideas in \cite{M}, to prove that under the right hypothesis for the Cantor sets and the function , the following formula holds
Cite
@article{arxiv.1911.03041,
title = {Scale Recurrence Lemma and Dimension Formula for Cantor Sets in the Complex Plane},
author = {Carlos Gustavo T. de A. Moreira and Alex Mauricio Zamudio},
journal= {arXiv preprint arXiv:1911.03041},
year = {2024}
}