Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations

Le Gal, O.; Sanz, F.; Speissegger, P.

doi:10.1090/S0002-9939-2013-11614-X

Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations
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by O. Le Gal, F. Sanz and P. Speissegger PDF

Proc. Amer. Math. Soc. 141 (2013), 2429-2438 Request permission

Abstract:

We consider a $2$-dimensional system of linear ordinary differential equations whose coefficients are definable in an o-minimal

structure $\mathcal {R}$. We prove that either every pair of solutions at 0 of the system is interlaced or the expansion of $\mathcal {R}$ by all solutions at 0 of the system is o-minimal. We also show that if the coefficients of the system have a Taylor development of sufficiently large finite order, then the question of which of the two cases holds can be effectively determined in terms of the coefficients of this Taylor development.

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