Critical intermittency in random interval maps

TL;DR

This paper investigates critical intermittency in random interval maps, revealing phase transitions in stationary measures and their properties, expanding understanding beyond classical neutral fixed point models.

Contribution

It introduces a new theory of critical intermittency for random interval maps, highlighting phase transitions and measure properties not previously studied.

Findings

Existence of phase transition in stationary measures

Stationary measure density is not in L^q for any q > 1

Properties of critical intermittency in random maps

Abstract

Critical intermittency stands for a type of intermittent dynamics in iterated function systems, caused by an interplay of a superstable fixed point and a repelling fixed point. We consider critical intermittency for iterated function systems of interval maps and demonstrate the existence of a phase transition when varying probabilities, where the absolutely continuous stationary measure changes between finite and infinite. We discuss further properties of this stationary measure and show that its density is not in $L^q$ for any $q > 1$. This provides a theory of critical intermittency alongside the theory for the well studied Manneville-Pomeau maps, where the intermittency is caused by a neutral fixed point.