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The Decoration Theorem for Mandelbrot and Multibrot Sets

The Decoration Theorem for Mandelbrot and Multibrot Sets

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.