Quasianalytic solutions of differential equations and o-minimal structures
| dc.creator | Rolin, J. -P. | |
| dc.creator | Sanz, F. | |
| dc.creator | Schaefke, R. | |
| dc.date | 2005-05-04 | |
| dc.date | 2006-06-02 | |
| dc.date.accessioned | 2026-07-07T06:39:53Z | |
| dc.date.available | 2026-07-07T06:39:53Z | |
| dc.description | It is well known that the non-spiraling leaves of real analytic foliations of codimension 1 all belong to the same o-minimal structure. Naturally, the question arises if the same statement is true for non-oscillating trajectories of real analytic vector fields. We show, under certain assumptions, that such a trajectory generates an o-minimal and model complete structure together with the analytic functions. The proof uses the asymptotic theory of irregular singular ordinary differential equations in order to establish a quasi-analyticity result from which the main theorem follows. As applications, we present an infinite family of o-minimal structures such that any two of them do not admit a common extension, and we construct a non-oscillating trajectory of a real analytic vector field in dimension 5 that is not definable in any o-minimal extension of the reals | |
| dc.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0505073 | |
| dc.identifier | http://arxiv.org/abs/math/0505073 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/101250 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Logic | |
| dc.subject | 03C64; 30D60; 34M40; 34M30 | |
| dc.title | Quasianalytic solutions of differential equations and o-minimal structures | |
| dc.type | text |