Turrittin's normal forms for linear systems of meromorphic ODEs over the real field

Abstract

We establish a version of Turrittin's result on normal forms of linear systems of meromorphic ODEs when the base eld K is real and closed. Both the proposed normal forms and the transformations used have coe cients in K. Our motivation comes from applications to the study of trajectories of real analytic vector elds (already treated in the literature in dimension three). For the sake of clarity and completeness, we rst review Turrittin's theorem in the case of an algebraically closed base eld.