Hyperbolic structure preserving isomorphisms of Markov shifts
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.
metric isomorphisms between Markov shifts
scientific article; zbMATH DE number 3996039
scientific article