Turrittin’s normal forms for linear systems of meromorphic ODEs over the real field. (English) Zbl 1527.34067
Summary: 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.
MSC:
| 34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |
| 34C08 | Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) |
| 34M03 | Linear ordinary differential equations and systems in the complex domain |
| 34M25 | Formal solutions and transform techniques for ordinary differential equations in the complex domain |
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