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arXiv · 1808.10408

On the inhomogeneity of the Mandelbrot set

Yusheng Luo
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Abstract

We will show the Mandelbrot set $M$ is locally conformally inhomogeneous: the only conformal map $f$ defined in an open set $U$ intersecting $\partial M$ and satisfying $f(U\cap\partial M)\subset \partial M$ is the identity map. The proof uses the study of local conformal symmetries of the Julia sets of polynomials: we will show in many cases, the dynamics can be recovered from the local conformal structure of the Julia sets.

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Yusheng Luo. 2018-08-30. On the inhomogeneity of the Mandelbrot set. https://doi.org/10.1093/imrn%2Frnz035

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