Complexity Characterization of Dynamical Systems Through Predictability

Details Complexity Characterization of Dynamical Systems Through Predictability Complexity Characterization of Dynamical Systems Through Predictability

2003-07-07

arxiv.org/abs/nlin/0307013v1

Acta Physica Polonica, vol.34, pag.3851 (2003)

Nonlinear Sciences

Chaotic Dynamics

26 pages, 5 eps-figures, Presented at the XV Marian Smoluchowski Symposium on Statistical Physics, Zakopane (Poland), Sept. 20

Scientific paper

Some aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a characterization of the unpredictability of a system gives a measure of its complexity. A special attention is devoted to finite-resolution effects on predictability, which can be accounted with suitable generalization of the standard indicators. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system.

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