From the 3 of 5 linked papers with an AI index.
5 papers
A technical note on the arithmetic cone of smooth periodic vector fields
Walid Oukil
The note shows that while periodic vector fields given by finite trigonometric polynomials have bounded deviation from a linear drift, this strong rotation property does not hold f…
Rigidity and Structural Asymmetry of Bounded Solutions
Walid Oukil
The paper studies a family of parametrized non‑homogeneous linear complex differential equations on the half‑line and shows that, under a specific rigidity condition, boundedness o…
From Scalar Rigidity to System Solutions and Abstract Prime Systems
Walid Oukil
We propose a unified framework for the Prime Rigidity Theory (PR), integrating three pillars: a scalar rigidity theorem for bounded solutions of non-homogeneous complex linear diff…
When Periodicity Fails to Guarantee the Existence of Rotation: A Counterexample on the 3-torus with a Nilpotent Linearization
Walid Oukil
The paper presents a smooth, periodic dynamical system on the 3‑torus whose weak rotation vector exists but the strong rotation vector fails, using a nilpotent Jacobian and infinit…
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…