Markovian, quasiperiodic and mixed dynamical systems

We study several models of base dynamics and linear cocycles over such systems. We establish effective rates of convergence of the Birkhoff averages oftoral translations. We derive large deviations estimates for mixed Markov-quasiperiodic dynamics. We prove continuity properties of the Lyapunov exponents of linear cocycles over Markov shifts. Besides their intrinsic interest,these results prepare the ground for a larger project concerned with the study of linear cocycles over mixed Markov-quasiperiodic base dynamics. As crucial steps in this study, we obtain a version of Kifer’s non random filtration and an upper large deviations estimate for such systems.