On entropy rates of dynamical systems and Gaussian processes

Milan Palus
School of Mathematics, Queensland University of Technology
GPO Box 2434, Brisbane, Qld 4001, Australia; and
Institute of Computer Science, Academy of Sciences of the Czech Republic
Pod vodárenskou vezí 2, 182 07 Prague 8, Czech Republic
E-mail: mp@uivt.cas.cz, mp@santafe.edu

Abstract:

A possibility of a relation between the Kolmogorov-Sinai entropy of a dynamical system and the entropy rate of a Gaussian process isospectral to time series generated by the dynamical system is numerically investigated using discrete and continuous chaotic dynamical systems. The results suggest that such a relation as a nonlinear one-to-one function may exist when the Kolmogorov-Sinai entropy varies smoothly with variations of system's parameters, but is broken in critical states near bifurcation points.