Non-interlaced solutions of 2-dimensional systems of linear ordinary differential equations Academic Article uri icon

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abstract

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

    structure R \mathcal {R} . We prove that either every pair of solutions at 0 of the system is interlaced or the expansion of R \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.

publication date

  • July 1, 2013