In this paper we characterize the mixing properties in the advection of passive tracers by exploiting the extreme value theory for dynamical systems. With respect to classical techniques directly related to the Poincare recurrences analysis, our meth
od provides reliable estimations of the characteristic mixing times and distinguishes between barriers and unstable fixed points. The method is based on a check of convergence for extreme value laws on finite datasets. We define the mixing times in terms of the shortest time intervals such that extremes converge to the asymptotic (known) parameters of the Generalized Extreme Value distribution. Our technique is suitable for applications in the analysis of other systems where mixing time scales need to be determined and limited datasets are available.
In this paper we prove the existence of Extreme Value Laws for dynamical systems perturbed by instrument-like-error, also called observational noise. An orbit perturbed with observational noise mimics the behavior of an instrumentally recorded time s
eries. Instrument characteristics - defined as precision and accuracy - act both by truncating and randomly displacing the real value of a measured observable. Here we analyze both these effects from a theoretical and numerical point of view. First we show that classical extreme value laws can be found for orbits of dynamical systems perturbed with observational noise. Then we present numerical experiments to support the theoretical findings and give an indication of the order of magnitude of the instrumental perturbations which cause relevant deviations from the extreme value laws observed in deterministic dynamical systems. Finally, we show that the observational noise preserves the structure of the deterministic attractor. This goes against the common assumption that random transformations cause the orbits asymptotically fill the ambient space with a loss of information about any fractal structures present on the attractor.
