The Homotopy Index and Partial Differential Equations

By:

Krzysztof P Rybakowski

Format:

Paperback / softback

Series:

Universitext

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Description

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.

Release date Australia

August 24th, 1987

Author

Krzysztof P Rybakowski

Audiences

Postgraduate, Research & Scholarly
Professional & Vocational
Undergraduate

Edition

Softcover reprint of the original 1st ed. 1987

Illustrations

XII, 208 p.

Pages

208

Series

Universitext

Dimensions

170x244x12

ISBN-13

9783540180678

Product ID

6112006

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