Artículo "Interlacing and separation of solutions of linear meromorphic ODEs"

Autores: Félix Álvaro Carnicero Martín y Fernando Sanz Sánchez

Aceptado para publicación en Proceedings of the International Conference
Dynamical Systems: 100 Years after Poincaré

Abstract: Solutions of two-dimensional linear systems of ODEs with real meromorphic coefficients 
may have two very distinct kinds of relative behaviour when they
approach to a singular point: either any two of them are linked or either any two of
them can be separated by a linear projection. In this paper, we are interesting in the
question of the decidability of the dichotomy linked/separated for the whole fam-
ily of systems. First, we rewrite the known result which asserts that the dichotomy
is determined in terms of a semialgebraic set (is decidable) on a truncation of the
Taylor expansion of the coefficients of the system. After that, we study the ques-
tion of the decidability of that dichotomy in terms of the coefficients of the system
themselves as elements of the ordered Hardy field of real meromorphic functions.