Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

The algorithmic information content for randomly perturbed systems

Pages: 921 - 934, Volume 4, Issue 4, November 2004      doi:10.3934/dcdsb.2004.4.921

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C. Bonanno - Department of Mathematics, University of Pisa, via Buonarroti, 2/a, 56127 Pisa, Italy (email)

Abstract: In this paper we prove estimates on the behaviour of the Kolmogorov-Sinai entropy relative to a partition for randomly perturbed dynamical systems. Our estimates use the entropy for the unperturbed system and are obtained using the notion of Algorithmic Information Content. The main result is an extension of known results to study time series obtained by the observation of real systems.

Keywords:  Random perturbation, Kolmogorov-Sinai entropy, information content.
Mathematics Subject Classification:  28D20, 37A50, 37M25, 60H40.

Received: January 2003;      Revised: March 2004;      Available Online: August 2004.