The Renormalization Method and Quadratic-Like Maps
Dynamical Systems
2016-09-06 v1
Abstract
The renormalization of a quadratic-like map is studied. The three-dimensional Yoccoz puzzle for an infinitely renormalizable quadratic-like map is discussed. For an unbranched quadratic-like map having the {\sl a priori} complex bounds, the local connectivity of its Julia set is proved by using the three-dimensional Yoccoz puzzle. The generalized version of Sullivan's sector theorem is discussed and is used to prove his result that the Feigenbaum quadratic polynomial has the {\sl a priori} complex bounds and is unbranched. A dense subset on the boundary of the Mandelbrot set is constructed so that for every point of the subset, the corresponding quadratic polynomial is unbranched and has the {\sl a priori} complex bounds.
Keywords
Cite
@article{arxiv.math/9511208,
title = {The Renormalization Method and Quadratic-Like Maps},
author = {Yunping Jiang},
journal= {arXiv preprint arXiv:math/9511208},
year = {2016}
}