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The Homotopy Index and Partial Differential Equations

  • Book
  • © 1987

Overview

Authors:
  1. Krzysztof P. Rybakowski

    1. Institut für Angewandte Mathematik, Albert-Ludwigs-Universität, Freiburg i. Br., Germany

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Part of the book series: Universitext (UTX)

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Table of contents (3 chapters)

  1. Front Matter

    Pages I-XII
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  2. The homotopy index theory

    • Krzysztof P. Rybakowski
    Pages 1-71

  3. Applications to partial differential equations

    • Krzysztof P. Rybakowski
    Pages 72-139

  4. Selected topics

    • Krzysztof P. Rybakowski
    Pages 140-194

  5. Back Matter

    Pages 195-208
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Keywords

About this book

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.

Authors and Affiliations

  • Institut für Angewandte Mathematik, Albert-Ludwigs-Universität, Freiburg i. Br., Germany

    Krzysztof P. Rybakowski

Bibliographic Information

  • Book Title: The Homotopy Index and Partial Differential Equations

  • Authors: Krzysztof P. Rybakowski

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-3-642-72833-4

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-18067-8Published: 24 August 1987

  • eBook ISBN: 978-3-642-72833-4Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XII, 208

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Analysis

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