Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Julia sets appear quasiconformally in the Mandelbrot set   In this paper we prove the following: Take any "small Mandelbrot set" and
zoom in a neighborhood of a parabolic or Misiurewicz parameter in it, then we
can see a quasiconformal image of a Cantor Julia set which is a perturbation of
a parabolic or Misiurewicz Julia set. Furthermore, zoom in its middle part,
then we can see a certain nested structure ("decoration") and finally another
"smaller Mandelbrot set" appears. A similar nested structure exists in the
Julia set for any parameter in the "smaller Mandelbrot set". We can also find
images of a Julia sets by quasiconformal maps with dilatation arbitrarily close
to 1. This answers a question by Adrian Douady. All the parameters belonging to
these images are semihyperbolic and this leads to the fact that the set of
semihyperbolic but non-Misiurewicz and non-hyperbolic parameters is dense with
Hausdorff dimension 2 in the boundary of the Mandelbrot set.

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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: acc-phys
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol