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arXiv · 1602.06281

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

S. Bonnot·A. de Carvalho·A. Messaoudi
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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 $(u,v) \mapsto (u+v,u)$.

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S. Bonnot, A. de Carvalho, A. Messaoudi. 2016-02-19. Julia sets for Fibonacci endomorphisms of $\mathbb{C}^2$ and $\mathbb{R}^2$. https://arxiv.org/abs/1602.06281

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