Homoclinic classes and finitude of attractors for vector fields on n-manifolds
| dc.creator | Carballo, C. M. | |
| dc.creator | Morales, C. A. | |
| dc.date | 2001-05-17 | |
| dc.date.accessioned | 2026-07-07T04:41:45Z | |
| dc.date.available | 2026-07-07T04:41:45Z | |
| dc.description | A homoclinic class of a vector field is the closure of the transverse homoclinic orbits associated to a hyperbolic periodic orbit. An attractor (a repeller) is a transitive set to which converges every positive (negative) nearby orbit. We show that a generic C1 vector field on a closed n-manifold has either infinitely many homoclinic classes or a finite collection of attractors (repellers) whose basins form an open-dense set. This result gives an approach to a conjecture by Palis. We also prove the existence of a locally residual subset of C1 vector fields on a 5-manifold having finitely many attractors and repellers but infinitely many homoclinic classes. | |
| dc.description | 12 pages, 3 figures | |
| dc.identifier | https://arxiv.org/abs/math/0105143 | |
| dc.identifier | http://arxiv.org/abs/math/0105143 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61486 | |
| dc.subject | Dynamical Systems | |
| dc.subject | 37C20 (Primary), 37C29 (Secondary) | |
| dc.title | Homoclinic classes and finitude of attractors for vector fields on n-manifolds | |
| dc.type | text |