Loss of memory and moment bounds for nonstationary intermittent dynamical systems

We study nonstationary intermittent dynamical systems, such as compositions of a (deterministic) sequence of Pomeau-Manneville maps. We prove two main results: sharp bounds on memory loss, including the "unexpected" faster rate for a large class of measures, and sharp moment bounds for Birkhoff sums and, more generally, "separately H\"older" observables.
Comment: 28 pages. v2: Incorporated referee suggestions. To appear in Communications in Mathematical Physics