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Generalizations of Douady’s magic formula

Published online by Cambridge University Press:  28 July 2021

Mathematics Institute, University of Warwick, Coventry, UK (email:
Department of Mathematics, University of Toronto, Toronto, Canada


We generalize a combinatorial formula of Douady from the main cardioid to other hyperbolic components H of the Mandelbrot set, constructing an explicit piecewise linear map which sends the set of angles of external rays landing on H to the set of angles of external rays landing on the real axis.

MSC classification

Original Article
© The Author(s), 2021. Published by Cambridge University Press

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