Zero level perturbation of a certain third-order linear solvable ODE\n with an irregular singularity at the origin of Poincar 'e rank 1

2016/09/16 by Tsvetana Stoyanova, Stoyanova, Tsvetana
Mathematics · Physics and Astronomy · #34A25 #34M03 #34M35 #34M40 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #Differential Equations and Numerical Methods #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1609.04949

openalex publication_date 2016/09/16 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We study an irregular singularity of Poincar 'e rank 1 at the origin of a\ncertain third-order linear solvable homogeneous ODE. We perturb the equation by\nintroducing a small parameter \ε\∈ (\ℝ₊, 0) ,(\ε <\n1) which causes the splitting of the irregular singularity into two finite\nFuchsian singularities. We show that when the solutions of the perturbed\nequation contain logarithmic terms, the Stokes matrices of the initial equation\nare limits of the part of the monodromy matrices around the finite resonant\nFuchsian singularities of the perturbed equation.\n

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