Dynamical Properties of Some Non-stationary, Non-simple Bratteli-Vershik Systems Public Deposited
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- March 20, 2019
- Affiliation: College of Arts and Sciences, Department of Mathematics
- Bratteli-Vershik systems, also called adics, are dynamical systems defined on the infinite path space of a Bratteli diagram. We introduce a family adics called limited scope adics for which the number of vertices increases by a constant at each level, and a subfamily determined by positive integer polynomials. We show that the dimension groups of the Bratteli diagrams associated to limited scope adics are intrinsically linked to the dynamics, generalizing a result for Cantor minimal systems, and we explicitly compute them for the subfamily of adics determined by a positive integer polynomials. We show that certain limited scope adics are isomorphic to subshifts. For the systems determined by positive integer polynomials we show that the set of fully-supported invariant ergodic probability measures consists of a one-parameter family of Bernoulli measures. We also show that the systems associated to positive integer polynomials are loosely Bernoulli. A particular limited scope adic system is the Euler adic system, for which the number of paths from the root vertex to a vertex (n,k) is the Eulerian number A(n,k). We show that this system has a unique fully-supported invariant ergodic probability measure and that the system is totally ergodic and loosely Bernoulli.
- Date of publication
- May 2006
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- Petersen, Karl Endel
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|Dynamical properties of some non-stationary, non-simple Bratteli-Vershik systems||2019-04-05||Public||