Dynamics of quadratic polynomials, I: Combinatorics and geometry of the Yoccoz puzzle
Dynamical Systems
2016-09-06 v1
Abstract
This work studies combinatorics and geometry of the Yoccoz puzzle for quadratic polynomials. It is proven that the moduli of the ``principal nest'' of annuli grow at linear rate. As a corollary we obtain complex a priori bounds and local connectivity of the Julia set for many infinitely renormalizable quadratics.
Cite
@article{arxiv.math/9503215,
title = {Dynamics of quadratic polynomials, I: Combinatorics and geometry of the Yoccoz puzzle},
author = {Mikhail Lyubich},
journal= {arXiv preprint arXiv:math/9503215},
year = {2016}
}