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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.15716 |
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| _version_ | 1866916034634579968 |
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| author | Oukil, Walid |
| author_facet | Oukil, Walid |
| contents | In this manuscript, 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 establishes a structural asymmetry: if two solutions with the same initial condition equal to $1$, corresponding respectively to the parameters $s$ and $1-\overline{s}$ lying in the critical strip, are both bounded on $[1,+\infty)$, then $\Re(s) = \tfrac{1}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15716 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Rigidity and Structural Asymmetry of Bounded Solutions Oukil, Walid Dynamical Systems In this manuscript, 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 establishes a structural asymmetry: if two solutions with the same initial condition equal to $1$, corresponding respectively to the parameters $s$ and $1-\overline{s}$ lying in the critical strip, are both bounded on $[1,+\infty)$, then $\Re(s) = \tfrac{1}{2}$. |
| title | Rigidity and Structural Asymmetry of Bounded Solutions |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2603.15716 |