  We provide formulas to compute the coefficients entering the affine scaling
needed to get a non-degenerate function for the asymptotic distribution of the
maxima of some kind of observable computed along the orbit of a randomly
perturbed dynamical system. This will give information on the local geometrical
properties of the stationary measure. We will consider systems perturbed with
additive noise and with observational noise. Moreover we will apply our
techniques to chaotic systems and to contractive systems, showing that both
share the same qualitative behavior when perturbed.
