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arXiv · 2510.01013

Julia sets appear quasiconformally in the Mandelbrot set, II: A parabolic proof

Tomoki Kawahira·Masashi Kisaka
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Abstract

Following the ideas of A.~Douady, we give an alternative proof of the authors' result: for any boundary point $c_0$ of the Mandelbrot set $M$, we can find small quasiconformal copies of $M$ in $M$ that are encaged in nested quasiconformal copies of the totally disconnected Julia set of a parameter arbitrarily close to $c_0$.

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Tomoki Kawahira, Masashi Kisaka. 2025-10-01. Julia sets appear quasiconformally in the Mandelbrot set, II: A parabolic proof. https://arxiv.org/abs/2510.01013

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