title: Extreme events in multivariate deterministic systems.
abstract: The probabilistic properties of extreme values in multivariate deterministic dynamical systems are analyzed. It is shown that owing to the intertwining of unstable and stable modes the effect of dynamical complexity on the extremes tends to be masked, in the sense that the cumulative probability distribution of typical variables is differentiable and its associated probability density is continuous. Still, there exist combinations of variables probing the dominant unstable modes displaying singular behavior in the form of nondifferentiability of the cumulative distributions of extremes on certain sets of phase space points. Analytic evaluations and extensive numerical simulations are carried out for characteristic examples of Kolmogorov-type systems, for low-dimensional chaotic flows, and for spatially extended systems.
authors.affiliation: Institut Royal Météorologique de Belgique, Brussels, Belgium. cnicolis@oma.be
authors.forename: C
authors.initials: C
authors.lastname: Nicolis
authors.forename: G
authors.initials: G
authors.lastname: Nicolis