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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On biaccessible points of the Mandelbrot set


Author: Saeed Zakeri
Journal: Proc. Amer. Math. Soc. 134 (2006), 2239-2250
MSC (2000): Primary 37F10, 37F20, 37F35, 35F45
Published electronically: March 14, 2006
MathSciNet review: 2213696
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Abstract: This paper provides a description for the quadratic polynomials on the boundary of the Mandelbrot set $ \mathcal M$ which are typical in the sense of harmonic measure. In particular, it is shown that a typical point on the boundary of $ \mathcal M$ has a unique parameter ray landing on it. Applications of this result in the study of embedded arcs in $ \mathcal M$ and the lamination associated with $ \mathcal M$ are given.


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Additional Information

Saeed Zakeri
Affiliation: Institute for Mathematical Sciences, Stony Brook University, Stony Brook, New York 11794
Address at time of publication: Department of Mathematics, Queens College of CUNY, Flushing, New York 11367
Email: zakeri@forbin.qc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08559-5
PII: S 0002-9939(06)08559-5
Received by editor(s): February 5, 2004
Received by editor(s) in revised form: January 24, 2005
Published electronically: March 14, 2006
Communicated by: Linda Keen
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.