Deformations of differential equations
Classical Analysis and ODEs
2025-09-04 v1 Algebraic Geometry
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.
Cite
@article{arxiv.2509.03285,
title = {Deformations of differential equations},
author = {Ziyu Zhang},
journal= {arXiv preprint arXiv:2509.03285},
year = {2025}
}