On biaccessible points of the Mandelbrot set

Zakeri, Saeed

doi:10.1090/S0002-9939-06-08559-5

On biaccessible points of the Mandelbrot set
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Proc. Amer. Math. Soc. 134 (2006), 2239-2250 Request permission

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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