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The explosion of singular hyperbolic attractors | C. A. Morales
; | Date: |
20 Mar 2003 | Subject: | Dynamical Systems MSC-class: Primary 37D30, Secondary 37D50 | math.DS | Abstract: | 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. | Source: | arXiv, math.DS/0303253 | Services: | Forum | Review | PDF | Favorites |
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