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math.DS2023
Dynamics of metrics in measure spaces and scaling entropy
A. M. Vershik, G. A. Veprev, P. B. Zatitskii
This survey is dedicated to a new direction in the theory of dynamical systems: the dynamics of metrics in measure spaces and new (catalytic) invariants of transformations with inv…
math.DS2019
On a universal Borel adic space
A. Vershik, P. Zatitskii
We prove that the so-called uniadic graph and its adic automorphism are Borel universal, i.e., every aperiodic Borel automorphism is isomorphic to the restriction of this automorph…
math.DS2017★ 7 cited
Universal adic approximation, invariant measures and scaled entropy
A. M. Vershik, P. B. Zatitskii
We define an infinite graded graph of ordered pairs and a~canonical action of the group (the adic action) and of the infinite sum of groups of order two~$\mathcal{D}=\…