The Square of a Map, Symbolic Dynamics, and the Conley Index
نویسنده
چکیده
We consider a map f from a locally compact metric space to itself, and use the discrete Conley index to study the difference between the local dynamics of f and f. In particular, we present a method, based on work by Mischaikow, Szymczak, et al., for detecting positive entropy symbolic dynamics by measuring the difference between Conley indices for f and f.
منابع مشابه
The Conley Index and Symbolic Dynamics
Suppose that N is an isolating neighborhood for S with respect to a continuous map f which decomposes into a disjoint union of nitely 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...
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