Morse equations and unstable manifolds of isolated invariant sets

Abstract

We describe a new way of obtaining the Morse equations of a Morse decomposition of an isolated invariant set. This is achieved through a filtration of truncated unstable manifolds associated with the decomposition. The results in the paper make it possible to calculate the Morse equations (and also the Conley index) in many interesting situations without using index pairs. We also study the intrinsic topology of the unstable manifold and obtain new duality properties of the cohomological Conley index.