Quenched Mixing Rates for Doubly Intermittent Maps

TL;DR

This paper investigates the mixing rates of certain random interval maps with indifferent fixed points, demonstrating polynomial decay of correlations through a novel random tower approach.

Contribution

Introduces a random tower construction to establish quenched mixing rates for maps with two indifferent fixed points and singularities, advancing understanding of their statistical properties.

Findings

Existence of equivariant absolutely continuous measures.

Polynomial decay of correlations proven.

Applicable to classes of maps with indifferent fixed points.

Abstract

We study quenched mixing rates for two classes of random interval maps characterized by the presence of two indifferent fixed points and singular points. Using a random tower construction we prove the existence of an equivariant absolutely continuous probability measures with polynomial decay of correlations.