We consider the quadratic family of maps given by faβ(x)=1βax2 with
xβ[β1,1], 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 X0β,X1β,..., given by Xnβ=fanβ, for
every integer nβ₯0, where each random variable Xnβ is distributed
according to the unique absolutely continuous, invariant probability of faβ.
Using techniques developed by Benedicks and Carleson, we show that the limiting
distribution of Mnβ=max{X0β,...,Xnβ1β} is the same as that which would
apply if the sequence X0β,X1β,... was independent and identically
distributed. This result allows us to conclude that the asymptotic distribution
of Mnβ is of Type III (Weibull).Comment: 18 page