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2004 Pasting Together Julia Sets: A Worked Out Example of Mating
John Milnor
Experiment. Math. 13(1): 55-92 (2004).

Abstract

The operation of "mating'' two suitable complex polynomial maps {\small $f_1$} and {\small $f_2$} constructs a new dynamical system by carefully pasting together the boundaries of their filled Julia sets so as to obtain a copy of the Riemann sphere, together with a rational map {\small $f_1 \mat f_2$} from this sphere to itself. This construction is particularly hard to visualize when the filled Julia sets {\small $K(f_i)$} are dendrites, with no interior. This note will work out an explicit example of this type, with effectively computable maps from {\small $K(f_1)$} and {\small $K(f_2)$} onto the Riemann sphere.

Citation

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John Milnor. "Pasting Together Julia Sets: A Worked Out Example of Mating." Experiment. Math. 13 (1) 55 - 92, 2004.

Information

Published: 2004
First available in Project Euclid: 10 June 2004

zbMATH: 1115.37051
MathSciNet: MR2065568

Subjects:
Primary: 37F45
Secondary: 30D05

Keywords: fractal tiling , Julia set , Lattès map

Rights: Copyright © 2004 A K Peters, Ltd.

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Vol.13 • No. 1 • 2004
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