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Mating, paper folding, and an endomorphism of \(\mathbb {PC}^2\). (English) Zbl 1408.37082
Summary: 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 \(\mathbb{PC}^2\) to itself. We show a relation between this rational function and an uncountable family of “paper folding” plane filling curves.

MSC:
37F15 Expanding holomorphic maps; hyperbolicity; structural stability of holomorphic dynamical systems
37F20 Combinatorics and topology in relation with holomorphic dynamical systems
37F50 Small divisors, rotation domains and linearization in holomorphic dynamics
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable
Software:
GAP; AutomGrp; automata; FR
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