RT info:eu-repo/semantics/article T1 Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations A1 Le Gal, O. A1 Sanz, F. A1 Speissegger, P. K1 Ordinary differential equations, o-minimal structures AB We consider a 2-dimensional system of linear ordinary differentialequations whose coefficients are definable in an o-minimal structure R. Weprove that either every pair of solutions at 0 of the system is interlaced or theexpansion of R by all solutions at 0 of the system is o-minimal. We also showthat if the coefficients of the system have a Taylor development of sufficientlylarge finite order, then the question of which of the two cases holds can beeffectively determined in terms of the coefficients of this Taylor development. PB AMS SN 0002-9939 YR 2013 FD 2013 LK https://uvadoc.uva.es/handle/10324/68179 UL https://uvadoc.uva.es/handle/10324/68179 LA eng NO PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 141, Number 7, July 2013, Pages 2429–2438 DS UVaDOC RD 18-nov-2024