An ordered structure of rank two related to Dulac's problem
| dc.creator | Dolich, Alf | |
| dc.creator | Speissegger, Patrick | |
| dc.date | 2006-03-02 | |
| dc.date | 2007-08-01 | |
| dc.date.accessioned | 2026-07-07T08:21:35Z | |
| dc.date.available | 2026-07-07T08:21:35Z | |
| dc.description | For a vector field F on the Euclidean plane we construct, under certain assumptions on F, an ordered model-theoretic structure associated to the flow of F. We do this in such a way that the set of all limit cycles of F is represented by a definable set. This allows us to give two restatements of Dulac's Problem for F--that is, the question whether F has finitely many limit cycles--in model-theoretic terms, one involving the recently developed notion of thorn-rank and the other involving the notion of o-minimality. | |
| dc.description | 45 pages, final version | |
| dc.identifier | https://arxiv.org/abs/math/0603052 | |
| dc.identifier | http://arxiv.org/abs/math/0603052 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/135365 | |
| dc.subject | Logic | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 37C27, 03C64 | |
| dc.title | An ordered structure of rank two related to Dulac's problem | |
| dc.type | text |