Estimating topological entropy via a symbolic data compression technique.
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 Hénon map, demonstrate that the convergence is fast: one obtains the theoretically correct topological entropy with a relatively short symbolic sequence.
Hirata
Yoshito
Y
Centre for Applied Dynamics and Optimization, Department of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia. yoshito@maths.uwa.edu.au
Mees
Alistair I
AI