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Journal of Dynamical and Control Systems
Published in: Journal of Dynamical and Control Systems 4/2018

08-05-2018

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

Author: Tsvetana Stoyanova

Published in: Journal of Dynamical and Control Systems | Issue 4/2018

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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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Literature
1.
Balser W. From divergent power series to analytic functions: theory and applications of multisummable power series, Vol. 1582. Heidelberg: Springer; 1994.
2.
Bateman H, Erdélyi A. 1953. Higher transcendental functions, Vol. 1: McGraw-Hill, New York.
3.
Duval A. Confluence procedures in the generalized hypergeometric family. J Math Sci Univ Tokyo 1998;5(4):597–625.MathSciNetMATH
4.
5.
Glutsyuk A. On the monodromy group of confluenting linear equation. Moscow Math J 2005;5(1):67–90.MathSciNetMATH
6.
Golubev V. Lectures on analytic theory of differential equations. Moscow: Gostekhizdat; 1950.MATH
7.
Horozov E, Stoyanova T. Non-integrability of some painlevé equations and dilogarithms. Regular Chaotic Dyn 2007;12:620–627.CrossRefMATH
8.
Hurtubise J, Lambert C, Rousseau C. Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of poincaré rank k. Moscow Math J 2013;14:309–338.MATH
9.
Ilyashenko Y, Yakovenko S. Lectures on analytic differential equations graduate studies in mathematics, Vol. 86. RI: American Mathematical Society, Providence; 2008.
10.
Iwasaki K, Kimura H, Shimomura S, Yoshida M. From Gauss to Painlevé, a modern theory of special functions aspects of mathematics, Vol. E16. Braunschweig: Friedr. Vieweg and Sohn; 1991.
11.
Kaplansky I. An introduction to differential algebra. Hermann: Publications L’institut de mathématique de l’université de Nancago; 1957.MATH
12.
Klimes M. Confluence of singularities of nonlinear differential equations via Borel-Laplace transformations. J Dynam Control Syst 2016;22:285–324.MathSciNetCrossRefMATH
13.
Klimes M. 2014. Analytic classification of families of linear differential systems unfolding a resonant irregular singularity. arXiv:1301.​5228.
14.
15.
Klimes M. 2017. Stokes phenomenon and confluence in non-autonomous Hamiltonian systems. arXiv:1709.​09078 [math.CA].
16.
Lambert C, Rousseau C. Complete system of analytic invariants for unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Moscow Math J 2012;12(1):77–138.MathSciNetMATH
17.
Lambert C, Rousseau C. Moduli space of unfolded differential linear systems with an irregular singularity of Poincaré rank 1. Moscow Math J 2013;13(3):529–550, 553-554.MATH
18.
Lambert C, Rousseau C. The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation. J Differential Equation 2008;244(10): 2641–2664.MathSciNetCrossRefMATH
19.
Martinet J, Ramis J-P. Théorie de Galois différentielle et resommation. In: Tournier E, editor. Computer Algebra and Differential equations. London: Academic; 1989, pp. 117–214.
20.
Mitschi C. Differential Galois groups of confluent generalized hypergeometric equations: an approach using Stokes multipliers. Pacific J Math 1996;176:365–405.MathSciNetCrossRefMATH
21.
22.
Ramis J-P. Séries divergentes et théories asymptotiques. Bull. Soc. Math. France 121 (1993) (suppl.) (Panoramas et Synthéses).
23.
Ramis J-P. Gevrey asymptotics and applications to holomorphic ordinary differential equations. In: Hua C and Wong R, editors. Differential Equations and Asymptotic Theory in Mathematical Physics (Series in Analysis vol 2). Singapore: World Scientific; 2004. p. 44-99.
24.
Remy P. Stokes phenomenon for single-level linear differential system: a perturbative approach. Funkcialaj Ekvacioj 2015;58:177–222.MathSciNetCrossRefMATH
25.
26.
Sibuya Y. Linear differential equations in the complex domain: problems of analytic continuation, Translations of Mathematical Monographs, 82. RI: American Mathematical Society, Providence; 1990.
27.
Slavyanov S, Lay W. Special functions: a unified theory based on singularities. Oxford: Oxford University Press; 2000.MATH
28.
29.
Stoyanova T. Non-integrability of painlevé V equation in the Liouville sense and Stokes phenomenon. Adv Pure Math 2011;1:170–183.CrossRefMATH
30.
31.
van der Put M, Singer M. Galois theory of linear differential equations, vol. 328 of Grundlehren der mathematischen Wissenshaften. Heidelberg: Springer; 2203.
32.
Wasow W. Asymptotic expansions for ordinary differential equations. New York: Dover; 1965.MATH
33.
Metadata
Title
Zero Level Perturbation of a Certain Third-Order Linear Solvable ODE with an Irregular Singularity at the Origin of Poincaré Rank 1
Author
Tsvetana Stoyanova
Publication date
08-05-2018
Publisher
Springer US
Published in
Journal of Dynamical and Control Systems / Issue 4/2018
Print ISSN: 1079-2724
Electronic ISSN: 1573-8698
DOI
https://doi.org/10.1007/s10883-018-9401-3

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