The Conley index and symbolic dynamics

Suppose that N is an isolating neighborhood for S with respect to a continuous map ƒ which decomposes into a disjoint union of finitely many compact sets. We establish a relationship between the Conley indices of subsets of S which appear in a natural way when studying the behavior of ƒ from the viewpoint of symbolic dynamics. The relationship is then used to prove a simple criterion for chaos in an isolated invariant set.