Extreme value theory for singular measures.

摘要: In this paper, we perform an analytical and numerical study of the extreme values specific observables dynamical systems possessing invariant singular measure. Such are expressed as functions distance orbit initial conditions with respect to a given point attractor. Using block maxima approach, show that extremes distributed according generalised value distribution, where parameters can be written information dimension The analysis is performed on few low dimensional maps. For Cantor ternary set Sierpinskij triangle, which constructed iterated function systems, inferred very good agreement theoretical values. strange attractors like those corresponding Lozi Henon maps, slower convergence distribution observed. Nevertheless, results in statistical estimates. It apparent allows for capturing fundamental geometrical structure attractor underlying system, basic reason being chosen act magnifying glass neighborhood from computed.