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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Additional Information
- O. Le Gal
- Affiliation: Laboratoire de Mathématiques, Bâtiment Chablais, Campus Scientifique, Université de Savoie, 73376 Le Bourget-du-Lac Cedex, France
- MR Author ID: 831839
- Email: olegal@agt.uva.es
- F. Sanz
- Affiliation: Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Valladolid, Prado de la Magdalena, s/n, E-47005 Valladolid, Spain
- MR Author ID: 623470
- Email: fsanz@agt.uva.es
- P. Speissegger
- Affiliation: Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada
- MR Author ID: 361060
- Email: speisseg@math.mcmaster.ca
- Received by editor(s): October 21, 2011
- Published electronically: March 28, 2013
- Communicated by: James E. Colliander
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2429-2438
- MSC (2010): Primary 34C08, 03C64
- DOI: https://doi.org/10.1090/S0002-9939-2013-11614-X
- MathSciNet review: 3043024