Borel–Cantelli lemmas and extreme value theory for geometric Lorenz models

Abstract

We establish dynamical Borel–Cantelli lemmas for nested balls and rectangles centered at generic points in the setting of geometric Lorenz maps. We also establish the convergence of rare events point processes to the standard Poisson process, which implies extreme value laws for observations maximised at generic points for geometric Lorenz maps. Further, we extend our extreme value laws to the associated flows.