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On equivalence of singularities of second order linear differential equations by point transformations
Martin Klimeš1
1 University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 3, pp. 527-560.

The article provides a local classification of singularities of meromorphic second order linear ordinary differential equations with respect to analytic/meromorphic linear point transformations, that is, transformations of both the unknown function and of the independent variable. In particular, it is shown that under a non-degeneracy condition two linear differential equations are analytically equivalent if and only if the associated companion systems are analytically equivalent as systems. Also the Lie algebras of analytic linear infinitesimal symmetries of the singularities are determined.

L’article propose une classification locale des singularités des équations différentielles linéaires du second ordre aux coefficients méromorphes par rapport aux transformations ponctuelles analytiques/méromorphes, c’est-à-dire, les transformations de la fonction inconnue aussi que de la variable indépendante. En particulier, il est montré que sous une condition de non-dégénérescence deux équations différentielles linéaires sont analytiquement équivalentes si et seulement si les systèmes compagnons associés sont analytiquement équivalents comme systèmes. Aussi les algèbres de Lie des symétries linéaires analytiques infinitésimales des singularités sont déterminées.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1684
Keywords: Linear ordinary differential equations, local analytic classification, normal forms, regular singularity, irregular singularity, Stokes phenomenon, analytic Lie symmetries
Keywords: Équations différentielles ordinaires linéaires, classification analytique locale, formes normalles, une singularité régulière, une singularité irrégulière, phénomène de Stokes, symétries de Lie analytiques

Martin Klimeš 1

1 University of Zagreb, Faculty of Electrical Engineering and Computing, Unska 3, 10000 Zagreb, Croatia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Martin Klimeš. On equivalence of singularities of second order linear differential equations by point transformations. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 30 (2021) no. 3, pp. 527-560. doi : 10.5802/afst.1684. https://afst.centre-mersenne.org/articles/10.5802/afst.1684/

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