Citation/Abstract

We study the dynamics of a continuous map on a locally compact metric space. Given a decomposition of an isolated invariant set into disjoint subsets, we assign a symbol to each subset and consider the resulting symbolic dynamics, where each word in the shift space is the itinerary of a point in the invariant set. We use the discrete Conley index to detect positive entropy sofic shifts contained in our shift space, by comparing the index of the entire invariant set to the sum of the indices of its pieces. We also consider generalizations to the case of a decomposition into subsets with nonempty intersection.