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SUMMARY:Extreme values for deterministic and random dynamical systems - Fr
 eitas\, JM (Centro de Matematica da Universidade do Porto)
DTSTART:20131218T140000Z
DTEND:20131218T150000Z
UID:TALK49372@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:It is well known that the Extremal Index (EI) measures the int
 ensity of clustering of extreme events in stationary processes. We sill se
 e that for some certain uniformly expanding systems there exists a dichoto
 my based on whether the rare events correspond to the entrance in small ba
 lls around a periodic point or a non-periodic point. In fact\, either ther
 e exists EI in $(0\,1)$ around (repelling) periodic points or the EI is eq
 ual to $1$ at every non-periodic point. The main assumption is that the sy
 stems have sufficient decay of correlations of observables in some Banach 
 space against all $L^1$-observables. Then we consider random perturbations
  of uniformly expanding systems\, such as piecewise expanding maps of the 
 circle. We will see that\, in this context\, for additive absolutely conti
 nuous noise (w.r.t. Lebesgue)\, the dichotomy vanishes and the EI is alway
 s 1.\n
LOCATION:Seminar Room 2\, Gatehouse Newton Institute
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