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Extreme Value distribution for singular measures
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
Hyperbolic Measures on Infinite Dimensional Spaces
Localization and dilation procedures are discussed for infinite dimensional
-concave measures on abstract locally convex spaces (following Borell's
hierarchy of hyperbolic measures).Comment: 25 Page
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