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External rays and the real slice of the Mandelbrot set

Published online by Cambridge University Press:  22 September 2003

SAEED ZAKERI
SAEED ZAKERI
Affiliation:
Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104-6395, USA (e-mail: [email protected]) Institute for Mathematical Sciences, Stony Brook University, Stony Brook, NY 11794-3651, USA
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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 tuned images of the real slice. Applications of these estimates in the study of critically non-recurrent real quadratics as well as bi-accessible points of quadratic Julia sets are given.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 2 , April 2003 , pp. 637 - 660
Copyright
2003 Cambridge University Press

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