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math.DS2022
Wiggle Island
Danny Calegari
A wiggle is an embedded curve in the plane that is the attractor of an iterated function system associated to a complex parameter z. We show the space of wiggles is disconnected --…
math.DS2022
Surgery sequences and self-similarity of the Mandelbrot set
Danny Calegari
We introduce an analog in the context of rational maps of the idea of hyperbolic Dehn surgery from the theory of Kleinian groups. A surgery sequence is a sequence of postcritically…