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Generalizations of Douady’s magic formula

Part of: Complex dynamical systems

Published online by Cambridge University Press:  28 July 2021

ADAM EPSTEIN  and
GIULIO TIOZZO Open the ORCID record for GIULIO TIOZZO [Opens in a new window]
ADAM EPSTEIN
Affiliation:
Mathematics Institute, University of Warwick, Coventry, UK (email: A.L.Epstein@warwick.ac.uk)
GIULIO TIOZZO*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Canada
*
email: tiozzo@math.utoronto.ca
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Abstract

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.

Keywords

Mandelbrot setexternal rayshyperbolic componentsmain cardioid

MSC classification

Primary: 37F20: Combinatorics and topology
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 42 , Issue 9 , September 2022 , pp. 2784 - 2799
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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