Lusternik-Schnirelmann category and Morse decompositions

Abstract

We study in this paper some properties of the Lusternik-Schnirelmann category of isolated invariant sets of continuous dynamical systems. There are several different definitions of this coefficient, although most of them agree in the important case of ANR's (Absolute Neighbourhood Retracts). We refer to the review articles [10] by R. H. Fox and [15, 16] by I. M. James for general information about this topological invariant. We shall use in this paper the definition of the Lusternik-Schnirelmann category of a compactum introduced by K. Borsuk in [4]