A theorem on the Markov periodic approximation in ergodic theory

DOI10.1007/BF02112330zbMath0559.47006OpenAlexW2029122848MaRDI QIDQ2266210

Anatoly M. Vershik

Publication date: 1985

Published in: Journal of Soviet Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02112330

zbMATH Keywords

simultaneous approximationmeasure preserving transformationoperator of multiplicationMarkov approximationperiodic automorphismsapproximation by periodic transformations

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Ergodic theory of linear operators (47A35)

Related Items

Dynamical directions in numeration, On the possible growth rate of a scaling entropy sequence, Limiting curves for the Pascal adic transformation, Locally semisimple algebras. Combinatorial theory and the \(K_ 0\)- functor, Bratteli diagrams where random orders are imperfect, Asymptotic theory of path spaces of graded graphs and its applications, Adic realizations of ergodic actions by homeomorphisms of Markov compacta and ordered Bratteli diagrams, Singularity and absolute continuity of measures associated with the rotation of a circle, Limiting curves for polynomial adic systems, Universal adic approximation, invariant measures and scaled entropy, Planar substitutions to Lebesgue type space-filling curves and relatively dense fractal-like sets in the plane, Self-similarity and spectral theory: on the spectrum of substitutions, The theory of filtrations of subalgebras, standardness, and independence, Dynamics of metrics in measure spaces and scaling entropy, Limiting curves for the dyadic odometer, A BRATTELI DIAGRAM FOR COMMUTING HOMEOMORPHISMS OF THE CANTOR SET, STRONG ORBIT EQUIVALENCE OF LOCALLY COMPACT CANTOR MINIMAL SYSTEMS, \(S\)-adic conjecture and Bratteli diagrams, SELF-SIMILAR CORRECTIONS TO THE ERGODIC THEOREM FOR THE PASCAL-ADIC TRANSFORMATION, Invariant measures and asymptotics for some skew products, Random deviations of ergodic sums for the Pascal adic transformation in the case of the Lebesgue measure, A sufficient condition for weak mixing of subtitutions and stationary adic transformations, On a universal Borel adic space, Orbit equivalence, flow equivalence and ordered cohomology, Recognizability for sequences of morphisms, Aperiodic orbits of piecewise rational rotations of convex polygons with recursive tiling, Interval exchange transformations over algebraic number fields: the cubic Arnoux–Yoccoz model

Cites Work

• The evolution of measures determined by the Navier-Stokes equations and on the solvability of the Cauchy problem for the Hopf statistical equation
• Theory of dynamical systems and general transformation groups with invariant measure
• Singularities of analytic foliations and characteristic classes
• The Canonical Measures for a Separable C * -Algebra
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item