Complex Systems

Entropy Estimates for Dynamical Systems Download PDF

Gerald Fahner
Peter Grassberger
Physics Department, Bergische Universität, Gesamthochschule Wuppertal,
Gauss-Strasse 20, Postfach 10027, 5600 Wuppertal 1, West Germany


We apply a method proposed recently for estimating entropies of symbol sequences to two ensembles of binary sequences obtained from dynamical systems. The first is the ensemble of (0,1)-sequences in a generating partition of the Henon map; the second is the ensemble of spatial strings in cellular automaton 22 in the statistically stationary state. In both cases, the entropy estimates agree with previous estimates. In the latter case, we confirm a previous claim that the entropy of spatial strings in rule 22 converges to zero, although extremely slowly.