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arXiv · 2509.03285

Deformations of differential equations

Ziyu Zhang
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Abstract

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.

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Ziyu Zhang. 2025-09-03. Deformations of differential equations. https://arxiv.org/abs/2509.03285

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