Infinite mixing for one-dimensional maps with an indifferent fixed point

Abstract

Abstract We study the properties of ‘infinite-volume mixing’ for two classes of intermittent maps: expanding maps with an indifferent fixed point at 0 preserving an infinite, absolutely continuous measure, and expanding maps with an indifferent fixed point at preserving the Lebesgue measure. All maps have full branches. While certain properties are easily adjudicated, the so-called global-local mixing, namely the decorrelation of a global and a local observable, is harder to prove. We do this for two subclasses of systems. The first subclass includes, among others, the Farey map. The second class includes the standard Pomeau–Manneville map mod 1. Morevoer, we use global-local mixing to prove certain limit theorems for our intermittent maps.