A priori bounds for some infinitely renormalizable quadratics: III. Molecules
Dynamical Systems
2007-12-17 v1
Abstract
In this paper we prove {\it a priori bounds} for infinitely renormalizable quadratic polynomials satisfying a ``molecule condition''. Roughly speaking, this condition ensures that the renormalization combinatorics stay away from the satellite types. These {\it a priori bounds} imply local connectivity of the corresponding Julia sets and the Mandelbrot set at the corresponding parameter values.
Keywords
Cite
@article{arxiv.0712.2444,
title = {A priori bounds for some infinitely renormalizable quadratics: III. Molecules},
author = {Jeremy Kahn and Mikhail Lyubich},
journal= {arXiv preprint arXiv:0712.2444},
year = {2007}
}