Calculating Topological Entropy for Transient Chaos with an Application to Communicating with Chaos

Recent work on communicating with chaos provides a practical motivation 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 convergence of the methods, we test them in situations where the topological entropy 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.