DCDS
Stochastic adding machine and $2$-dimensional Julia sets
Ali Messaoudi Rafael Asmat Uceda
In this work we define a stochastic adding machine associated to a quadratic base $(F_n)_{n \geq 0}$ formed by recurrent sequences of order 2. We obtain a Markov chain with states in $\mathbb{Z}^+$ and we prove that the spectrum of the transition operator associated to this Markov chain is connected to the filled Julia sets for a class of endomorphisms in $\mathbb{C}^2$ of which we study topological properties.
keywords: recurrent sequence Julia sets stochastic adding machines spectrum of transition operator. Markov chains
DCDS
On the Fibonacci complex dynamical systems
El Houcein El Abdalaoui Sylvain Bonnot Ali Messaoudi Olivier Sester
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 $c\in\mathbb{C}$ 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.
keywords: holomorphic motion endomorphisms of $\mathbb{C}^2$. Julia sets quasi-circle complex dynamics

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