The Decoration Theorem for Mandelbrot and Multibrot Sets

Dzmitry Dudko

doi:10.1093/imrn/rnw135

The Decoration Theorem for Mandelbrot and Multibrot Sets

Dzmitry Dudko

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove the decoration theorem for the Mandelbrot set (and Multibrot sets) which says that when a "little Mandelbrot set" is removed from the Mandelbrot set, then most of the resulting connected components have small diameters. By universality of the Mandelbrot set similar results hold for quadratic-like families.

Original language	English
Pages (from-to)	3985-4028
Number of pages	44
Journal	International Mathematics Research Notices
Volume	2017
Issue number	13
DOIs	https://doi.org/10.1093/imrn/rnw135
State	Published - Jul 1 2017

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AB - We prove the decoration theorem for the Mandelbrot set (and Multibrot sets) which says that when a "little Mandelbrot set" is removed from the Mandelbrot set, then most of the resulting connected components have small diameters. By universality of the Mandelbrot set similar results hold for quadratic-like families.

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The Decoration Theorem for Mandelbrot and Multibrot Sets

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