Examples of Feigenbaum Julia sets with small Hausdorff dimension
Dynamical Systems
2007-05-23 v1 Complex Variables
Abstract
We give examples of infinitely renormalizable quadratic polynomials with stationary combinatorics whose Julia sets have Hausdorff dimension arbitrar y close to 1. The combinatorics of the renormalization involved is close to the Chebyshev one . The argument is based upon a new tool, a ``Recursive Quadratic Estimate'' for the Poincar\'e series of an infinitely re normalizable map.
Cite
@article{arxiv.math/0407066,
title = {Examples of Feigenbaum Julia sets with small Hausdorff dimension},
author = {Artur Avila and Mikhail Lyubich},
journal= {arXiv preprint arXiv:math/0407066},
year = {2007}
}
Comments
13 pages