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Shape and Conley Index of Attractors and Isolated Invariant Sets

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Differential Equations, Chaos and Variational Problems

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 75))

Abstract

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.

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Author information

Authors and Affiliations

  1. Facultad de Matemáticas, Universidad Complutense, E-28040, Madrid, Spain

    José M. R. Sanjurjo

Authors
  1. José M. R. Sanjurjo
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Vasile Staicu

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Dedicated to A. Cellina and J. Yorke

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© 2007 Birkhäuser Verlag Basel/Switzerland

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Sanjurjo, J.M.R. (2007). Shape and Conley Index of Attractors and Isolated Invariant Sets. In: Staicu, V. (eds) Differential Equations, Chaos and Variational Problems. Progress in Nonlinear Differential Equations and Their Applications, vol 75. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8482-1_29

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