Improved polynomial rates of memory loss for nonstationary intermittent dynamical systems

We study nonstationary dynamical systems formed by sequential concatenation of nonuniformly expanding maps with a uniformly expanding first return map. Assuming a polynomially decaying upper bound on the tails of first return times that is nonuniform with respect to location in the sequence, we derive a corresponding sharp polynomial rate of memory loss. As applications, we obtain new estimates on the rate of memory loss for random ergodic compositions of Pomeau--Manneville type intermittent maps and intermittent maps with unbounded derivatives.