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Conformal Geometry and Dynamics

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Mating, paper folding, and an endomorphism of $ \mathbb{P}\mathbb{C}^2$


Author: Volodymyr Nekrashevych
Journal: Conform. Geom. Dyn. 20 (2016), 303-358
MSC (2010): Primary 37F15, 37F20
DOI: https://doi.org/10.1090/ecgd/302
Published electronically: November 22, 2016
MathSciNet review: 3574443
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Abstract: We are studying topological properties of the Julia set of the map $ F(z, p)=\left (\left (\frac {2z}{p+1}-1\right )^2, \left (\frac {p-1}{p+1}\right )^2\right )$ of the complex projective plane $ \mathbb{P}\mathbb{C}^2$ to itself. We show a relation between this rational function and an uncountable family of ``paper folding'' plane filling curves.


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DOI: https://doi.org/10.1090/ecgd/302
Received by editor(s): March 2, 2016
Received by editor(s) in revised form: September 15, 2016
Published electronically: November 22, 2016
Dedicated: In memory of Vitaly Sushchansky
Article copyright: © Copyright 2016 American Mathematical Society