External rays and the real slice of the Mandelbrot set

Details External rays and the real slice of the Mandelbrot set External rays and the real slice of the Mandelbrot set

2002-10-24

arxiv.org/abs/math/0210382v1

Mathematics

Dynamical Systems

22 pages, 4 figures

Scientific paper

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.

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