Critical intermittency in random interval maps

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. 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.