Suppose that N is an isolating neighborhood for S with respect to a continuous map f 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 f from the viewpoint of symbolic dynamics. The relationship is then used to prove a simple criterion for chaos in an isolated invariant set.
Szymczak, A. (1996). The Conley index and symbolic dynamics. Topology, 35(2), 287–299. https://doi.org/10.1016/0040-9383(95)00029-1