# Julia sets appear quasiconformally in the Mandelbrot set

@article{Kawahira2018JuliaSA, title={Julia sets appear quasiconformally in the Mandelbrot set}, author={Tomoki Kawahira and Masashi Kisaka}, journal={arXiv: Dynamical Systems}, year={2018} }

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…

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Renormalization and embedded Julia sets in the Mandelbrot set

- 2018

The decorations of a small Mandelbrot set within the Mandelbrot set M contain embedded Julia sets; these are Cantor sets quasiconformally homeomorphic to a quadratic Julia set. So the local geometry…

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