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The Homotopy Index And Partial Differential Equations by K. Rybakowski

The Homotopy Index And Partial Differential Equations

by K. Rybakowski
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Book cover type: Paperback
  • ISBN13: 9783540180678
  • Binding: Paperback
  • Subject: Mathematics and Statistics
  • Publisher: Springer Verlag
  • Publisher Imprint: Springer V
  • Publication Date:
  • Pages: 687
  • Original Price: EUR 94.99
  • Language: English
  • Edition: N/A
  • Item Weight: 363 grams
  • BISAC Subject(s): Geometry / General, Topology, and Mathematical Analysis

The homotopy index theory was developed by Charles Conley for two- sided flows on compact spaces. The homotopy or Conley index, which provides an algebraic-topologi- cal measure of an isolated invariant set, is defined to be the ho- motopy type of the quotient space N /N, where is a certain 1 2 1 2 compact pair, called an index pair. Roughly speaking, N1 isolates the invariant set and N2 is the "exit ramp" of N . 1 It is shown that the index is independent of the choice of the in- dex pair and is invariant under homotopic perturbations of the flow. Moreover, the homotopy index generalizes the Morse index of a nQnde- generate critical point p with respect to a gradient flow on a com- pact manifold. In fact if the Morse index of p is k, then the homo- topy index of the invariant set {p} is Ik - the homotopy type of the pointed k-dimensional unit sphere.

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