Deformations of differential equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916931015016448 |
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| author | Zhang, Ziyu |
| author_facet | Zhang, Ziyu |
| contents | We study perturbations of linear differential equations, deriving explicit series solutions, using Dyson-type expansions. We analyze the monodromy of deformed solutions in a number of examples, and relate this to cocycles in a cohomological framework. We also analyze the spectral properties of the hypergeometric equation under infinitesimal deformations, derive the first-order eigenvalue correction via orthogonality, and establish natural bounds for the perturbed problem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_03285 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformations of differential equations Zhang, Ziyu Classical Analysis and ODEs Algebraic Geometry We study perturbations of linear differential equations, deriving explicit series solutions, using Dyson-type expansions. We analyze the monodromy of deformed solutions in a number of examples, and relate this to cocycles in a cohomological framework. We also analyze the spectral properties of the hypergeometric equation under infinitesimal deformations, derive the first-order eigenvalue correction via orthogonality, and establish natural bounds for the perturbed problem. |
| title | Deformations of differential equations |
| topic | Classical Analysis and ODEs Algebraic Geometry |
| url | https://arxiv.org/abs/2509.03285 |