Mating, paper folding, and an endomorphism of PC^2

Abstract

We are studying topological properties of the Julia set of the map $F(z,p)=((2z/(p+1)-1{)}^2,((p-1)/(p+1){)}^2)$ of the complex projective plane $P{C}^2$ to itself. We show a relation of this rational function with an uncountable family of "paper folding" plane filling curves.

53 pages, 36 figures

References in corpus (3)

• Thurston equivalence of topological polynomials
• Iterated Monodromy Groups of Quadratic Polynomials, I
• Combinatorial models of expanding dynamical systems