Springer
The Homotopy Index and Partial Differential Equations
Product Code:
9783540180678
ISBN13:
9783540180678
Condition:
New
$61.47
The Homotopy Index and Partial Differential Equations
$61.47
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.
| Author: Krzysztof P. Rybakowski |
| Publisher: Springer |
| Publication Date: Aug 24, 1987 |
| Number of Pages: 208 pages |
| Binding: Paperback or Softback |
| ISBN-10: 3540180672 |
| ISBN-13: 9783540180678 |
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