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.

Item Information Item Information

Format: Trade Paperback
Author: Rybakowski, Krzysztof P.
ISBN: 9783540180678
Condition: Used
Dimensions: 9.61 x 0.47
Number Of Pages: 208
Publication Year: 1987

The Homotopy Index and Partial Differential Equations

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