Turrittin's Theorem revisited. The real case

Moulay Barkatou, Félix Álvaro Carnicero-Martín, Fernando Sanz Sánchez

Published 2023-05-14Version 1

We establish a real version of Turrittin's result on polynomial and formal normal forms of linear systems of ODEs with meromorphic coefficients. Both the normal forms or the transformations used have only real coefficients. In order to adapt the proofs to the real case, we make a review of the result in the complex case.