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Singular Continuations of Attractors

Giraldo, A. and Rodríguez Sanjurjo, José Manuel (2009) Singular Continuations of Attractors. SIAM journal on applied dynamical systems, 8 (2). pp. 554-575. ISSN 1536-0040

Official URL: http://epubs.siam.org/doi/pdf/10.1137/080737356

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Abstract

We study dynamical and topological properties of the singularities of continuations of attractors of flows on manifolds. Despite the fact that these singularities are not isolated invariant sets, they share many of the properties of attractors; in particular, they have finitely generated Cech homology and cohomology, and they have the Cech homotopy type of attractors. This means that, from a global point of view, the singularities of continuations are topological objects closely related to finite polyhedra. The global structure is preserved even for weaker forms of continuation. An interesting case occurs with the Lorenz system for parameter values close to the situation of preturbulence. A general result, motivated by this particular case, is presented.


Item Type:Article
Uncontrolled Keywords:Lyapunov functions and stability; attractors, repellers
Subjects:Sciences > Mathematics > Geometry
Sciences > Mathematics > Topology
ID Code:16780
Deposited On:19 Oct 2012 08:55
Last Modified:19 Oct 2012 08:55

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