Finite equivalence for countable state Markov shifts
by
Doris Fiebig
University of Heidelberg

Parry showed that two transitive shifts of finite type (SFT) have a common finite-to-1 extension by a transitive SFT iff they have the same entropy. A factor map between transitive SFTs is finite-to-1 iff it is entropy preserving. Thus two transitive SFTs with the same entropy admit a common entropy preserving extension. We extend this version of Parry's result to transitive locally compact Markov shifts. We show furthermore that the factor maps can be chosen countable-to-1 biclosing in general.

Date received: February 26, 1998