The Homotopy Index and Partial Differential Equations (Paperback, Softcover reprint of the original 1st ed. 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."

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Universitext
Release date:	August 1987
First published:	1987
Authors:	Krzysztof P Rybakowski
Dimensions:	244 x 170 x 12mm (L x W x T)
Format:	Paperback
Pages:	208
Edition:	Softcover reprint of the original 1st ed. 1987
ISBN-13:	978-3-540-18067-8
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations Books > Science & Mathematics > Mathematics > Geometry > General Books > Science & Mathematics > Mathematics > Topology > General
LSN:	3-540-18067-2
Barcode:	9783540180678

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