Geodesic
Universal adic approximation, invariant measures and scaled entropy
Izvestiya. Mathematics , Tome 81 (2017) no. 4, pp. 734-770

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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.
Keywords: graph of ordered pairs, universal action, scaled entropy.
Mots-clés : adic transformation 
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     title = {Universal adic approximation, invariant measures and scaled entropy},
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A. M. Vershik; P. B. Zatitskii. Universal adic approximation, invariant measures and scaled entropy. Izvestiya. Mathematics , Tome 81 (2017) no. 4, pp. 734-770. http://geodesic.mathdoc.fr/item/IM2_2017_81_4_a2/