CALCULATING TOPOLOGICAL-ENTROPY FOR TRANSIENT CHAOS WITH AN APPLICATION TO COMMUNICATING WITH CHAOS

Recent work on communicating with chaos provides a practical motivatio n for being able to determine numerically the topological entropy for chaotic invariant sets. In this paper we discuss numerical methods for evaluating topological entropy. To assess the accuracy and convergenc e of the methods, we test them in situations where the topological ent ropy is known independently. We also discuss the entropy of invariant chaotic saddles formed by those points in a given attractor that never visit some forbidden ''gap'' region. Such gaps have been proposed as a means of providing noise immunity in schemes for communication with chaos, and we discuss the dependence of the topological entropy on the size of the gap.