Construction of Symbolic Dynamics from Experimental Time Series

Symbolic dynamics plays a central role in the description of the evolution of nonlinear systems. However, there are few reliable methods for determining the symbolic dynamics of chaotic experimental time series. One of the major di culties is that the experimental data contains both the chaotic dynamics of the underlying deterministic system and the random uctuations produced by stochastic perturbations associated with the experimental process. Using data obtained from a magnetoelastic ribbon experiment we show how a new approach based on topological techniques can be used to obtain a description of the dynamics in terms of subshift dynamics on a nite set of symbols. These topological methods have been developed in a way that allows for the inclusion of experimental error and the existence of bounded noise.