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Interlacing and Separation of Solutions of Linear Meromorphic ODEs

  • Félix Álvaro CarniceroEmail author
  • Fernando Sanz
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 54)

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 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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Departamento de Álgebra, Análisis Matemático, Geometría y Topología, Facultad de CienciasUniversity of ValladolidValladolidSpain

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