Computing the Kolmogorov entropy from time signals of dissipative and conservative dynamical systems

Abstract

The extraction of the Kolmogorov (metric) entropy from an experimental time signal is discussed. Theoretically we stress the concept of generators and that the existence of an expansive constant guarantees that a finite-time series would be sufficient for the calculation of the metric entropy. On the basis of the theory we attempt to propose optimal algorithms which are tested on a number of examples. The approach is applicable to both dissipative and conservative dynamical systems.