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

S. Bonnot; A. de Carvalho; A. Messaoudi

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

Dynamical Systems 2016-02-22 v1

Authors: S. Bonnot , A. de Carvalho , A. Messaoudi

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 $(u,v) \mapsto (u+v,u)$ .

Keywords

julia set holomorphic dynamics

Cite

@article{arxiv.1602.06281,
  title  = {Julia sets for Fibonacci endomorphisms of $\mathbb{C}^2$ and $\mathbb{R}^2$},
  author = {S. Bonnot and A. de Carvalho and A. Messaoudi},
  journal= {arXiv preprint arXiv:1602.06281},
  year   = {2016}
}

Comments

34 pages, 12 figures

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