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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.

Inhaltsverzeichnis

Frontmatter

Chapter I. The homotopy index theory

Abstract
In this chapter we develop the concepts of the categorial Morse index and the homotopy index.
Krzysztof P. Rybakowski

Chapter II. Applications to partial differential equations

Abstract
We will now give a few applications of the theory developed in Chapter I. First we describe some of the types of differential operators which generate sectorial operators.
Krzysztof P. Rybakowski

Chapter III. Selected topics

Abstract
We begin this chapter by the study of the inner structure of an invariant set.
Krzysztof P. Rybakowski

Backmatter

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