Rigidity and Structural Asymmetry of Bounded Solutions

Walid Oukil

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arXiv · 2603.15716

Rigidity and Structural Asymmetry of Bounded Solutions

Walid Oukil

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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 induces 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 $\Re(s)=\tfrac12$.

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Walid Oukil. 2026-03-16. Rigidity and Structural Asymmetry of Bounded Solutions. https://arxiv.org/abs/2603.15716

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