Julia sets for Fibonacci endomorphisms of $\mathbb{C}^2$ and   $\mathbb{R}^2$
  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 $(u,v) \mapsto (u+v,u)$. 
S. Bonnot, A. de Carvalho, A. Messaoudi
math.DS