On the components of the unstable set of isolated invariant sets

Abstract

The aim of this note is to shed some light on the topological structure of the unstable set of an isolated invariant set K. We give a bound on the number of essential quasicomponents of the unstable set of K in terms of the homological Conley index of K. The proof relies on an explicit pairing between Čech homology classes and Alexander–Spanier cohomology classes that takes the form of an integral.