Improved polynomial rates of memory loss for nonstationary intermittent dynamical systems

TL;DR

This paper establishes sharp polynomial rates of memory loss for nonstationary dynamical systems formed by concatenating nonuniformly expanding maps, with applications to intermittent maps with unbounded derivatives.

Contribution

It introduces a new method to derive precise polynomial memory loss rates for nonstationary systems with nonuniform tail bounds, extending previous results to more general settings.

Findings

Derived sharp polynomial decay rates of memory loss.

Applied results to random compositions of intermittent maps.

Provided new estimates for systems with unbounded derivatives.

Abstract

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.