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Predictability: a way to characterize complexity

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Cencini,  M.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

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Citation

Boffetta, G., Cencini, M., Falcioni, M., & Vulpiani, A. (2002). Predictability: a way to characterize complexity. Physics Reports-Review Section of Physics Letters, 356(6), 367-474. Retrieved from http://www.sciencedirect.com/science?_ob=IssueURL&_tockey=%23TOC%235540%232002%23996439993%23272648%23FLA%23Volume_356,_Issue_6,_Pages_367-476_(January_2002)&_auth=y&view=c&_acct=C000002818&_version=1&_urlVersion=0&_userid=42421&md5=7dfac3b20dab1b7989e9b0afdbdd1f96.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-3848-5
Abstract
Different 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. Adopting this point of view, we review some developments in the characterization of the predictability of systems showing different kinds of complexity: from low-dimensional systems to high-dimensional ones with spatio-temporal chaos and to fully developed turbulence. A special attention is devoted to finite-time and 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. The characterization of irregular behavior in systems with discrete phase space is also considered. (C) 2002 Elsevier Science B.V. All rights reserved.