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arXiv · 1304.4864

On the Fibonacci complex dynamical systems

El Houcein El Abdalaoui·Sylvain Bonnot·Ali Messaoudi·Olivier Sester
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Abstract

We consider in this paper a sequence of complex analytic functions constructed by the following procedure $f_n(z)=f_{n-1}(z)f_{n-2}(z)+c$, where $c\in\C$ is a parameter. Our aim is to give a thorough dynamical study of this family, in particular we are able to extend the familiar notions of Julia sets and Green function and to analyze their properties. As a consequence, we extend some well-known results. Finally we study in detail the case where $c$ is small.

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El Houcein El Abdalaoui, Sylvain Bonnot, Ali Messaoudi, Olivier Sester. 2013-04-17. On the Fibonacci complex dynamical systems. https://arxiv.org/abs/1304.4864

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