Global-local mixing for the Boole map

Abstract

In the context of \u2018infinite-volume mixing\u2019 we prove global-local mixing for the Boole map, a.k.a. Boole transformation, which is the prototype of a non-uniformly expanding map with two neutral fixed points. Global-local mixing amounts to the decorrelation of all pairs of global and local observables. In terms of the equilibrium properties of the system it means that the evolution of every absolutely continuous probability measure converges, in a certain precise sense, to an averaging functional over the entire space