Multipliers of periodic orbits of quadratic polynomials and the parameter plane
Dynamical Systems
2007-05-23 v1 Complex Variables
Abstract
We prove an extension results for the multiplier of an attracting periodic orbit of a quadratic map as a function of the parameter. This has applications to the problem of geometry of the Mandelbrot and Julia sets. In particular, we prove that the size of p/q-limb of a hyperbolic component of the Mandelbrot set of period n is O(4^n/p), and give an explicit condition on internal arguments under which the Julia set of corresponding (unique) infinitely renormalizable quadratic polynomial is not locally connected
Cite
@article{arxiv.math/0702011,
title = {Multipliers of periodic orbits of quadratic polynomials and the parameter plane},
author = {Genadi Levin},
journal= {arXiv preprint arXiv:math/0702011},
year = {2007}
}
Comments
28 pages, no figures