We consider stochastic processes arising from dynamical systems by evaluating an observable
function along the orbits of the system. We review some results about the existence of Extreme Value
Laws for such processes with special emphasis on the clustering effect associated to observables achieving
a global maximum at a periodic point. Then we consider recent developments where the observables have
multiple maximal points which are correlated or bound by belonging to the same orbit of a certain chosen point.
These multiple correlated maxima can be seen as a new mechanism creating clustering which we will explore.
The systems considered include expanding maps of the interval such as Rychlik maps but also maps with an
indifferent fixed point such as Manneville-Pommeau maps.
Clustering of extreme events created by periodic and fake periodic dynamics
Jorge Freitas