Universal adic approximation, invariant measures and scaled entropy

Abstract

We define an infinite graded graph of ordered pairs and a~canonical action of the group $\mathbb{Z}$ (the adic action) and of the infinite sum of groups of order two~$\mathcal{D}={\sum }_1^{\infty }\mathbb{Z}/2\mathbb{Z}$ on the path space of the graph. It is proved that these actions are universal for both groups in the following sense: every ergodic action of these groups with invariant measure and binomial generator, multiplied by a~special action (the `odometer'), is metrically isomorphic to the canonical adic action on the path space of the graph with a~central measure. We consider a~series of related problems.

32 pp. Ref 31

References in corpus (1)

• Geometry and Dynamics of Admissible Metrics in Measure Spaces