A Borel-Cantelli lemma for non-stationary dynamical systems

Abstract: In this thesis we present a Borel–Cantelli lemma for dynamical systems such that the dynamics driving the system varies with time. These results are largely based on a decomposition of transfer operators produced by Rychlik. Some limitations on the structure of sequences that is necessary for the results is given some discussion. Two examples of systems that could be considered are presented, one of which is accompanied by a method by Liverani for bounding rates of decay.