Probabilistic potential theory and induction of dynamical systems

Abstract

In this article, we outline a version of a balayage formula in probabilistic potential theory adapted to measure-preserving dynamical systems. This balayage identity generalizes the property that induced maps preserve the restriction of the original invariant measure. As an application, we prove in some cases the invariance under induction of the Green-Kubo formula, as well as the invariance of a new degree 3 invariant.