Shape and Conley index of attractors and isolated invariant sets



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Rodríguez Sanjurjo, José Manuel (2008) Shape and Conley index of attractors and isolated invariant sets. In Differential equations, chaos and variational problems. Progress in Nonlinear Differential Equations and their Applications (75). Birkhäuser, Basel, pp. 393-406. ISBN 978-3-7643-8481-4

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This article is an exposition of several results concerning the theory of continuous dynamical systems, in which Topology plays a key role. We study homological and homotopical properties of attractors and isolated invariant compacta as well as properties of their unstable manifolds endowed with the intrinsic topology. We also provide a dynamical framework to express properties which are studied in Topology under the name of Hopf duality. Finally we see how the use of the intrinsic topology makes it possible to calculate the Conley-Zehnder equations of a Morse decomposition of an isolated invariant compactum, provided we have enough information about its unstable manifold.

Item Type:Book Section
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Papers from the Conference "Views on ODEs" held in Aveiro, June 2006

Subjects:Sciences > Mathematics > Differential equations
ID Code:21792
Deposited On:11 Jun 2013 12:34
Last Modified:04 Sep 2020 09:14

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