English

On the Fibonacci complex dynamical systems

Dynamical Systems 2013-04-18 v1

Abstract

We consider in this paper a sequence of complex analytic functions constructed by the following procedure fn(z)=fn1(z)fn2(z)+cf_n(z)=f_{n-1}(z)f_{n-2}(z)+c, where c\Cc\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 cc is small.

Keywords

Cite

@article{arxiv.1304.4864,
  title  = {On the Fibonacci complex dynamical systems},
  author = {El Houcein El Abdalaoui and Sylvain Bonnot and Ali Messaoudi and Olivier Sester},
  journal= {arXiv preprint arXiv:1304.4864},
  year   = {2013}
}

Comments

26 pages, 5 figures

R2 v1 2026-06-22T00:01:44.485Z