Deformations of differential equations

2025/09/03 by Ziyu Zhang, Zhang, Ziyu
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2509.03285

openalex publication_date 2025/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Isomonodromy transformations of linear systems of difference equations

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