5 papers
A technical note on the arithmetic cone of smooth periodic vector fields
Walid Oukil
The present note identifies the fundamental mechanism governing the extension of the contraction method. Although every periodic vector field defined by a finite trigonometric poly…
Asymmetry of a class of Mellin transforms
Walid Oukil
We consider a class of Mellin transforms associated with a class of functions , defined for every complex in the critical strip. We establish sufficient conditions on…
From scalar rigidity to abstract prime set and abstract integer system
Walid Oukil
We propose a unified framework for Prime Rigidity Theory (PR) by introducing the notions of an "abstract integer system" and an "abstract prime set", consisting, respectively, of t…
When Periodicity Fails to Guarantee the Existence of Rotation: A Counterexample on the 3-torus with a Nilpotent Linearization
Walid Oukil
In this manuscript, we construct an explicit counterexample of smooth infinitely differentiable, periodic dynamical system on the 3-torus for which the rotation vector exists in th…
Exponential stable manifold for the synchronized state of the abstract mean field system
Walid Oukil
This paper investigates the exponential stability of abstract mean field systems in their synchronized state. We analyze stability by studying the linearized system and demonstrate…