Shape and Conley Index of Attractors and Isolated Invariant Sets

  • José M. R. Sanjurjo
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 75)


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.


Unstable Manifold Global Attractor Conley Index Morse Decomposition Compact Global Attractor 
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© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  • José M. R. Sanjurjo
    • 1
  1. 1.Facultad de MatemáticasUniversidad ComplutenseMadridSpain

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