Research
My publications, ongoing projects, and master's thesis
Master's Thesis (Mémoire)
On the Stability of Discrete Dynamical Systems in Metric Spaces
Advisor: [Advisor Name]
Institution: University of Mila, Algeria
Expected completion: June 2026
This thesis investigates the stability properties of discrete dynamical systems on complete metric spaces. We develop new sufficient conditions for asymptotic stability using fixed-point theorems and Lyapunov-type functions, generalizing classical results by relaxing smoothness requirements on the underlying maps.
Download Thesis (PDF)Current Projects
Stability Analysis via Generalized Lyapunov Functions
Developing a framework for constructing generalized Lyapunov functions for discrete dynamical systems on non-compact metric spaces. This extends classical Lyapunov stability theory to broader classes of maps.
Topological Conjugacy Classification
Investigating conditions under which two dynamical systems on topological spaces are topologically conjugate. Using symbolic dynamics to establish constructive conjugacy results for classes of expanding maps.
Publications & Preprints
On the Stability of Discrete Dynamical Systems in Metric Spaces
Abdelouahab Mostafa, Advisor Name
A Note on Topological Conjugacy of Expanding Maps on the Circle
Abdelouahab Mostafa
Integral Inequalities and Their Applications to Differential Equations
Abdelouahab Mostafa, Collaborator Name