Hyperbolic structure preserving isomorphisms of Markov shifts
type: Item
instance of: scholarly article
title: Hyperbolic structure preserving isomorphisms of Markov shifts
zbMATH Open document ID: 0615.28011
DOI: 10.1007/BF02801996
author: Klaus Schmidt
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: The author investigates metric isomorphisms between Markov shifts which preserve the hyperbolic structure modulo null sets. Such isomorphisms have certain group invariants (which earlier were investigated by \textit{W. Krieger} [Z. Wahrscheinlichkeitstheor. Verw. Geb. 65, 323-328 (1983; Zbl 0506.60059)], \textit{W. Parry} [Bull. Lond. Math. Soc. 11, 170-176 (1979; Zbl 0425.60029)] and \textit{W. Parry} and \textit{K. Schmidt} [Invent. Math. 76, 15-32 (1984; Zbl 0563.28008)]. Finitary isomorphisms need not preserve the hyperbolic structure, however they do, if they have finite expected code (and inverse code) lengths.
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 60J99
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 3996039
zbMATH Keywords: metric isomorphisms between Markov shifts
zbMATH Keywords: hyperbolic structure
zbMATH Keywords: Finitary isomorphisms
reviewed by: Manfred Denker
MaRDI profile type: Publication
cites work: An information cocycle for groups of non-singular transformations
cites work: An amenable equivalence relation is generated by a single transformation
cites work: A class of C*-algebras and topological Markov chains
cites work: Ergodic Equivalence Relations, Cohomology, and Von Neumann Algebras. I
cites work: Q3958514
cites work: On dimension functions and topological Markov chains
cites work: On the finitary isomorphisms of markov shifts that have finite expected coding time
cites work: Coboundaries and Homomorphisms for Non-Singular Actions and a Problem of H. Helson
cites work: Finitary Isomorphisms with Finite Expected Code Lengths
cites work: Natural coefficients and invariants for Markov-shifts
cites work: Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions
cites work: Invariants for finitary isomorphisms with finite expected code lengths
cites work: Conditional pressure and coding
cites work: A Dimension, Dimension Modules, and Markov Chains
full work available at URL: https://doi.org/10.1007/bf02801996
OpenAlex ID: W4249896418
description: scientific article; zbMATH DE number 3996039