Interlacing and Separation of Solutions of Linear Meromorphic ODEs
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 family 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 question 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.
- 4.Dieudonné, J.: Éléments d’analyse. Tome I: Fondements de l’analyse moderne. Gauthier-Villars, Éditeur, Paris (1968)Google Scholar
- 6.Miller, C.: Basics of O-minimality and Hardy Fields. In: Lecture Notes on O-minimal Structures and Real Analytic Geometry. Fields Institute Communications, vol. 62. Springer, New York (2012)Google Scholar