The Homotopy Index and Partial Differential Equations

di Krzysztof P. Rybakowski (Autore)

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG, 1987

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.

• Autore: Krzysztof P. Rybakowski
• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Collana: Universitext
• Anno: 1987
• Rilegatura: Paperback / softback
• Pagine: 208 p.
• Dimensioni: 244 x 170 mm
• EAN: 9783540180678

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