arXiv subjects

A. Messaoudi

Publications and source records attributed to A. Messaoudi.

4 recordsLinked to original sources

arXiv2026

Shadowing and Stability of Non-Invertible $p$-adic Dynamics

The stability theory of compact metric spaces with positive topological dimension is a well-established area in Dynamical Systems. A central result, attributed to Walters, connects the concepts of topological stability and the shadowing property in invertible dynamics. In contrast, zero-dimensional stability theory is a developing field, with an analogue of Walters' theorem for Cantor spaces being fully established only in 2019 by Kawaguchi. In this paper, we investigate the shadowing and stability properties of non-invertible dynamics in zero-dimensional spaces, focusing on the $p$-adic integers $\mathbb{Z}_{p} $ and the $p$-adic numbers $\mathbb{Q}_{p}$, where $p \geq 2$ is a prime number. The main result provides sufficient conditions under which the following families of maps exhibit strong shadowing and stability properties: 1) $p$-adic dynamical systems that are right-invertible through contractions, and 2) left-invertible contractions. Consequently, new examples of stable $p$-adic dynamics are presented.

math.NT↗

arXiv2016

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

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

math.DS↗

arXiv2014

A class of cubic Rauzy Fractals

In this paper, we study arithmetical and topological properties for a class of Rauzy fractals ${\mathcal R}_a$ given by the polynomial $x^3- ax^2+x-1$ where $a \geq 2$ is an integer. In particular, we prove the number of neighbors of ${\mathcal R}_a$ in the periodic tiling is equal to $8$. We also give explicitly an automaton that generates the boundary of ${\mathcal R}_a$. As a consequence, we prove that ${\mathcal R}_2$ is homeomorphic to a topological disk.

math.DS↗

arXiv2011

On the spectrum of stochastic perturbations of the shift and Julia sets

We extend the Killeen-Taylor study in \cite{KT} by investigating in different Banach spaces ($\ell^α(\N), c_0(\N),c_c(\N)$) the point, continuous and residual spectra of stochastic perturbations of the shift operator associated to the stochastic adding machine in base 2 and in Fibonacci base. For the base 2, the spectra are connected to the Julia set of a quadratic map. In the Fibonacci case, the spectra involve the Julia set of an endomorphism of $\C^2$.

math.DS↗