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Zero Level Perturbation of a Certain Third-Order Linear Solvable ODE with an Irregular Singularity at the Origin of Poincaré Rank 1

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Abstract

We study an irregular singularity of Poincaré rank 1 at the origin of a certain third-order linear solvable homogeneous ODE. We perturb the equation by introducing a small parameter \(\varepsilon \in ({\mathbb R}_{+},0)\) (ε < 1), which causes the splitting of the irregular singularity into two finite Fuchsian singularities. We show that when the solutions of the perturbed equation contain logarithmic terms, the Stokes matrices of the initial equation are limits of the part of the monodromy matrices around the finite resonant Fuchsian singularities of the perturbed equation.

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Acknowledgments

The author thanks the referee for valuable suggestions and comments, which led to the simplification and clarification of the paper. The author is grateful to L. Gavrilov and E. Horozov for helpful discussions and comments.

Funding

The author was partially supported by Grant DN 02-5/2016 of the Bulgarian Fond “Scientific Research.”

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Sofia University, 5 J. Bourchier Blvd., 1164, Sofia, Bulgaria

    Tsvetana Stoyanova

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  1. Tsvetana Stoyanova
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Stoyanova, T. Zero Level Perturbation of a Certain Third-Order Linear Solvable ODE with an Irregular Singularity at the Origin of Poincaré Rank 1. J Dyn Control Syst 24, 511–539 (2018). https://doi.org/10.1007/s10883-018-9401-3

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  • DOI: https://doi.org/10.1007/s10883-018-9401-3

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