Mating, paper folding, and an endomorphism of ℙℂ²

Nekrashevych, Volodymyr

doi:10.1090/ecgd/302

Mating, paper folding, and an endomorphism of $\mathbb {P}\mathbb {C}^2$
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Conform. Geom. Dyn. 20 (2016), 303-358 Request permission

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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