Sampling local properties of attractors via Extreme Value Theory |
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| Institution: | 1. Mathematical Sciences Institute, Australian National University, Canberra, Australia;2. Departmento de Matemática Aplicada, Escuela de Ingeniería y Arquitectur, Universidad de Zaragoza, C/ María de Luna 3, Zaragoza 50018, Spain;1. GeoRessources (UMR 7359), Université de Lorraine-ENSG/CNRS/CREGU, Vandoeuvre-lès-Nancy F-54518, France;2. Gocad Research Group - ASGA, Vandoeuvre-lès-Nancy F-54518, France;3. CNRS, CRPG, UPR2300, 15 Rue Notre Dame des Pauvres, Vandoeuvre-lès-Nancy F-54501, France;4. Université de Lorraine, ENSG, INP, Rue Doyen Marcel Roubault, Vandoeuvre-lès-Nancy F-54501, France;1. Earth Science Institute, Geological Division, Slovak Academy of Sciences, Dúbravská cesta 9, P.O. Box 106, 840 05 Bratislava 45, Slovak Republic |
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| Abstract: | We provide formulas to compute the coefficients entering the affine scaling needed to get a non-degenerate function for the asymptotic distribution of the maxima of some kind of observable computed along the orbit of a randomly perturbed dynamical system. This will give information on the local geometrical properties of the stationary measure. We will consider systems perturbed with additive noise and with observational noise. Moreover we will apply our techniques to chaotic systems and to contractive systems, showing that both share the same qualitative behavior when perturbed. |
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