We show how to rewrite the celebrated theory of Poincare recurrences in terms of classical extreme value laws whose parameters depend on the geometrical and dynamical properties of the system analysed. We show that, for generic points of the attractor, the extreme value laws do not depend on how the extremes are selected. On the other hand, for unstable fixed points, an explicit dependence on the selection method appears, so that one has a useful way to characterize the behavior of the dynamics around them.

SPEC, CEA Saclay