The Homotopy Index and Partial Differential Equations - Couverture souple

Rybakowski, Krzysztof P.

Couverture souple

ISBN 10 : 3540180672 ISBN 13 : 9783540180678

Editeur : Springer-Verlag, 1987

Synopsis

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.

Détails de l'édition

• Éditeur: Springer-Verlag
• Date d'édition: 1987
• Langue: anglais
• ISBN 10: 3540180672
• ISBN 13: 9783540180678
• Reliure: Broché
• Nombre de pages: 224
• Coordonnées du fabricant: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Allemagne