Julia sets for Fibonacci endomorphisms of ${\mathbb{C}}^2$ and ${\mathbb{R}}^2$

Abstract

We study the dynamics of the family $f_c(x,y)=(xy+c,x)$ of endomorphisms of ${\mathbb{R}}^2$ and ${\mathbb{C}}^2$, where $c$ is a real or complex parameter. Such maps can be seen as perturbations of the map $f_0(x,y)=(xy,x)$, which is a complexification of the Anosov torus map $(u,v)\mapsto (u+v,u)$.

34 pages, 12 figures