External rays and the real slice of the Mandelbrot set

Saeed Zakeri

External rays and the real slice of the Mandelbrot set

Dynamical Systems 2007-05-23 v1 Complex Variables

Authors: Saeed Zakeri

Abstract

This paper investigates the set of angles of the parameter rays which land on the real slice $[-2,1/4]$ of the Mandelbrot set. We prove that this set has zero length but Hausdorff dimension 1. We obtain the corresponding results for the tuned images of the real slice. Applications of these estimates in the study of critically non-recurrent real quadratics as well as biaccessible points of quadratic Julia sets are given.

Keywords

Mandelbrot set real slice external rays Hausdorff dimension parameter rays Julia sets quadratic maps

Cite

@article{arxiv.math/0210382,
  title  = {External rays and the real slice of the Mandelbrot set},
  author = {Saeed Zakeri},
  journal= {arXiv preprint arXiv:math/0210382},
  year   = {2007}
}

Comments

22 pages, 4 figures

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