abstract: Quasistatic dynamical systems (QDS), introduced by Dobbs and Stenlund around 2015, model dynamics that slowly transform over time due to external influences. They can be viewed as generalizations of conventional dynamical systems, and belong to the realm of deterministic non-stationary processes.
In this talk I will explain the basics of QDSs, and then explore ergodic and distributional properties in the case where the time-evolution is specified by intermittent maps of Pomeau-Manneville type. I will discuss a proof for a functional central limit theorem, which is based on solving a well-posed martingale problem and relies heavily on the cone technique of Liverani-Saussol-Vaienti. In the process I obtain tools of independent interest, and I will present some implications of these through Stein’s method to multivariate normal approximation of non-stationary intermittent systems.