Electronic Journal of Differential Equations, Vol. 2023 (2023), No. 79, pp. 1-23.

Title: Turrittin's normal forms for linear systems of meromorphic ODEs over the real field
       
Authors: Moulay Barkatou (Univ. de Limoges, France)
         Felix A. Carnicero (Univ. de Valladolid, Spain)
         Fernando Sanzs (Univ. de Valladolid, Spain)

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.