Moulay Barkatou, Felix A. Carnicero, Fernando Sanzs Sanchez
Abstract:
We establish a version of Turrittin's result on normal forms of linear systems
of meromorphic ODEs when the base field K is real and closed.
Both the proposed normal forms and the transformations used have coefficients
in K. Our motivation comes from applications to the study of trajectories
of real analytic vector fields (already treated in the literature in dimension
three). For the sake of clarity and completeness, we first review Turrittin's
theorem in the case of an algebraically closed base field.
Submitted July 4, 2023. Published November 27, 2023.
Math Subject Classifications: 34C20, 34C08, 34M03, 34M25.
Key Words: Linear systems of meromorphic ODE; formal normal form; Turrittin's theorem.
DOI: 10.58997/ejde.2023.79
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Moulay Barkatou XLIM, Université de Limoges CNRS, 123, Av. A. Thomas 87060 Limoges cedex, France email: moulay.barkatou@unilim.fr |
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Félix A. Carnicero Departamento de Algebra, Análisis Matemático, Geometría y Topología Universidad de Valladolid Facultad de Ciencias. Paseo de Belén, 7, E-47011 Valladolid, Spain} email: carnicero_fac@hotmail.com |
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Fernando Sanzs Sánchez Departamento de Algebra, Análisis Matemático, Geometría y Topología Universidad de Valladolid Facultad de Ciencias Paseo de Belén, 7, E-47011 Valladolid, Spainā email: fsanz@uva.es |
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