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main cardioid

Ergodic Theory and Dynamical Systems (1)

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1 results

Generalizations of Douady’s magic formula
Part of
- Complex dynamical systems
ADAM EPSTEIN, GIULIO TIOZZO
Journal:

Ergodic Theory and Dynamical Systems / Volume 42 / Issue 9 / September 2022

Published online by Cambridge University Press:

28 July 2021, pp. 2784-2799

Print publication:

September 2022
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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.