Statistical Properties of Chaotic Dynamical Systems: Extreme Value Theory and Borel-cantelli Lemmas

In this thesis, we establish extreme value (EV) theory and dynamical BorelCantelli lemmas for a class of deterministic chaotic dynamical systems. We establish the distributional convergence (to the three classical extreme value distributions) of the scaled sequence of partial maxima of some time series arising from an observable on systems such as the planar dispersing billiards, Lozi-like maps, and compact group skew-extensions of non-uniformly hyperbolic base maps with Hölder cocyles. We also establish Borel-Cantelli lemmas for a large class of one-dimensional non-uniformly expanding maps, and for these, we also obtain an almost sure characterization of the exceedences of the sequence of partial maxima.