Loss of memory and moment bounds for nonstationary intermittent dynamical systems

TL;DR

This paper investigates nonstationary intermittent dynamical systems, providing sharp bounds on memory loss and moment bounds for Birkhoff sums, revealing faster decay rates and detailed statistical properties.

Contribution

It introduces new sharp bounds on memory loss and moment bounds for nonstationary intermittent systems, including compositions of Pomeau-Manneville maps, with novel faster decay rates.

Findings

Faster decay rates for memory loss in certain measures

Sharp bounds on Birkhoff sum moments

Applicability to compositions of Pomeau-Manneville maps

Abstract

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.