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ISSN 1088-6826(e) ISSN 0002-9939(p)

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
Posted: March 14, 2006
MathSciNet review: 2213696
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Abstract | References | Similar Articles | Additional Information

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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