Abstract
A theory of extremes is developed for chaotic dynamical systems and illustrated on representative models of fully developed chaos and intermitent chaos. The cumulative distribution and its associated density for the largest value occurring in a data set, for monotonically increasing (or decreasing) sequences, and for local maxima are evaluated both analytically and numerically. Substantial differences from the classical statistical theory of extremes are found, arising from the deterministic origin of the underlying dynamics.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
K. Lindenberg and B. J. West,J. Stat. Phys. 42:201 (1986).
T. A. Buishand,Stat. Neerland. 43:1 (1989).
E. J. Gumbel,Statistics of Extremes (Columbia University Press, New York, 1958).
J. Galambos,The Asymptotic Theory of Extreme Order Statistics (Wiley, New York 1978).
M. R. Leadbetter and H. Rootzén,Ann. Prob. 16:431 (1988).
M. R. Leadbetter, G. Lindgren, and H. Rootzén,Extremes and Related Properties of Random Sequences and Processes (Springer-Verlag, New York, 1983).
G. Nicolis and I. Prigogine,Exploring Complexity (Freeman, San Francisco, 1989).
C. Nicolis and G. Nicolis, eds.,Irreversible Phenomena and Dynamical Systems Analysis in the Geosciences (Reidel, Dordrecht, 1987).
E. N. Lorenz,Tellus 36A:98 (1984).
P. Bergé, Y. Pomeau, and C. Vidal,L'ordre dans le chaos (Hermann, Paris, 1984).
H. G. Schuster,Deterministic Chaos, 2nd ed. (VCH Verlag, Weinheim, 1988).
C. Gyorgyi and P. Szepfalusy,Z. Phys. B. Cond. Matter 55:179 (1984).
P. C. Hemmer,J. Phys. A: Math. Gen. 17:L247 (1984).
N. G. de Bruijn,Asymptotic Methods in Analysis (Dover, New York, 1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Balakrishnan, V., Nicolis, C. & Nicolis, G. Extreme value distributions in chaotic dynamics. J Stat Phys 80, 307–336 (1995). https://doi.org/10.1007/BF02178361
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02178361