Estimating topological entropy via a symbolic data compression technique - art. no. 026205

摘要

We estimate topological entropy via symbolic dynamics using a data compression technique called the context-tree weighting method. Unlike other symbolic dynamical approaches, which often have to choose ad hoc parameters such as the depth of a tree, the context-tree weighting method is almost parameter-free and infers the transition structure of the system as well as transition probabilities. Our examples, including a Markov model, the logistic map, and the Henon map, demonstrate that the convergence is fast: one obtains the theoretically correct topological entropy with a relatively short symbolic sequence. [References: 24]