Doubly Intermittent Full Branch Maps with Critical Points and Singularities

TL;DR

This paper investigates a class of one-dimensional maps with complex dynamics, including indifferent fixed points and singularities, establishing the existence of unique invariant measures, their mixing properties, decay rates, and limit theorems.

Contribution

It introduces a new class of full branch maps with critical points and singularities, proving the existence and properties of their invariant measures.

Findings

Existence of a unique invariant mixing absolutely continuous measure

Quantitative decay of correlation rates

Validation of limit theorems for the system

Abstract

We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely continuous probability measures, study its rate of decay of correlation and prove a number of limit theorems.