Extreme value distribution for singular measures

Lucarini, V. ORCID: https://orcid.org/0000-0001-9392-1471, Faranda, D., Turchetti, G. and Vaienti, S. (2012) Extreme value distribution for singular measures. Chaos, 22 (2). 023135. ISSN 1089-7682 doi: 10.1063/1.4718935

Abstract/Summary

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/27142
Item Type	Article
Refereed	Yes
Divisions	Interdisciplinary Research Centres (IDRCs) > Walker Institute Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	American Institute of Physics
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