 99240 Wolf Jung
 Families of Homeomorphic Subsets of the Mandelbrot Set
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Jun 23, 99

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Abstract. The $1/3$limb of the Mandelbrot set $M$ is considered as
a graph, where the vertices are given by certain Misiurewicz points.
The edges are described as a union of building blocks that are called
"frames". There is a 11 correspondence between these frames and
starshaped subsets of the Julia set $K_a$, where $a$ denotes the
Misiurewicz point $\gamma_M(11/56)$. This global combinatorial
correspondence between $M_{1/3}$ and $K_a$ provides a complement
to the asymptotic similarity obtained by Tan Lei.
The frames are defined by recursions for external angles or parapuzzles.
By quasiconformal surgery we construct a homeomorphism $h$ of the edge from
$a$ to $\gamma_M(23/112)$ onto itself, and show that the frames on this edge
are homeomorphic. This can be generalized to all edges of $\M_{1/3}$, and
to all limbs of $\M$.
The method is similar to that of BrannerDouady and BrannerFagella,
but the construction of the "first return map" is different.
The reader is invited to obtain the related program mandel.exe from
http://www.iram.rwthaachen.de/~jung/ .
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