Universitext

The Homotopy Index and Partial Differential Equations

Authors: Rybakowski, Krzysztof

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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.

Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook $89.00
price for USA in USD
  • ISBN 978-3-642-72833-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • Immediate eBook download after purchase and usable on all devices
  • Bulk discounts available
Softcover $119.00
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
The Homotopy Index and Partial Differential Equations
Authors
Series Title
Universitext
Copyright
1987
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-72833-4
DOI
10.1007/978-3-642-72833-4
Softcover ISBN
978-3-540-18067-8
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XII, 208
Topics