Lusternik-Schnirelmann category, Hopf duality, and isolated invariant sets

Abstract

We establish an inequality relating the Lusternik-Schnirelmann coefficient of the unstable manifold of an isolated invariant set of a flow and the coefficients of a Morse decomposition of this set. We also establish some homological relations between the Morse sets of a particular Morse decomposition of an isolated invariant set. This result introduces Hopf duality properties in the context of continuous dynamical systems.