Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842138 | Nonlinear Analysis: Theory, Methods & Applications | 2010 | 5 Pages |
Abstract
Topological properties of the domain of attraction for dynamical systems are investigated. The main purpose of this paper is to prove that a compact, asymptotically stable attractor of a dynamical system defined on a locally compact metric space is a deformation retract of its domain of attraction, in a weak sense that is made precise. Under additional local assumptions, the attractor can be shown to be a retract, a deformation retract, or a strong deformation retract. The well known result that the domain of attraction of an asymptotically stable equilibrium is contractible follows as a corollary.
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Authors
Emmanuel Moulay, Sanjay P. Bhat,