Abstract (EN):
We consider the quadratic family of maps given by f(a)(x) = 1 - ax(2) with x epsilon [- 1, 1], where a is a Benedicks-Carleson parameter. For each of these chaotic dynamical systems we study the extreme value distribution of the stationary stochastic processes X(0), X(1), ..., given by X(n) = f(a)(n), for every integer n >= 0, where each random variable Xn is distributed according to the unique absolutely continuous, invariant probability of f(a). Using techniques developed by Benedicks and Carleson, we show that the limiting distribution of M(n) = max {X(0), ..., X(n) - 1} is the same as that which would apply if the sequence X(0), X(1), ... was independent and identically distributed. This result allows us to conclude that the asymptotic distribution of M(n) is of type III (Weibull).
Idioma:
Inglês
Tipo (Avaliação Docente):
Científica
Contacto:
amoreira@fep.up.pt; jmfreita@jc.up.pt
Nº de páginas:
17