The explosion of singular hyperbolic attractors
| dc.creator | Morales, C. A. | |
| dc.date | 2003-03-20 | |
| dc.date | 2003-03-26 | |
| dc.date.accessioned | 2026-07-07T04:56:14Z | |
| dc.date.available | 2026-07-07T04:56:14Z | |
| dc.description | A {\em singular hyperbolic attractor} for flows is a partially hyperbolic attractor with singularities (hyperbolic ones) and volume expanding central direction \cite{mpp1}. The geometric Lorenz attractor \cite{gw} is an example of a singular hyperbolic attractor. In this paper we study the perturbations of singular hyperbolic attractors for three-dimensional flows. It is proved that any attractor obtained from such perturbations contains a singularity. So, there is an upper bound for the number of attractors obtained from such perturbations. Furthermore, every three-dimensional flow $C^r$ close to one exhibiting a singular hyperbolic attractor has a singularity non isolated in the non wandering set. We also give sufficient conditions for a singularity of a three-dimensional flow to be stably non isolated in the nonwandering set. These results generalize well known properties of the Lorenz attractor. | |
| dc.identifier | https://arxiv.org/abs/math/0303253 | |
| dc.identifier | http://arxiv.org/abs/math/0303253 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/66847 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Primary 37D30, Secondary 37D50 | |
| dc.title | The explosion of singular hyperbolic attractors | |
| dc.type | text |