Rigidity and Structural Asymmetry of Bounded Solutions

Walid Oukil

dynamical systems

Rigidity and Structural Asymmetry of Bounded Solutions

arXiv:2603.15716

summary

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 of two related solutions forces the complex parameter to have real part 1/2.

Abstract

We introduce a family of parametrized non-homogeneous linear complex differential equations on $[1, \infty)$ , depending on a complex parameter. We identify a "Rotation number hypothesis" on the non-homogeneous term, which a structural asymmetry between the solutions corresponding to the parameters $s$ and $1 - s$ . More precisely, if both solutions with initial value $1$ are bounded on $[1, + \infty)$ , then necessarily $ℜ (s) = \frac{1}{2}$ .

Topics & keywords

#differential equations #complex analysis #rigidity #asymmetry #spectral conditionsnon‑homogeneous linear complex ODErotation number hypothesisbounded solutionsrigidity inequalityparameter s