UNSPECIFIED (1993) MIXING SETS AND RELATIVE ENTROPIES FOR HIGHER-DIMENSIONAL MARKOV SHIFTS. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 13 (Part 4). pp. 705-735. ISSN 0143-3857

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Abstract

We consider certain measurable isomorphism invariants for measure-preserving Z(d)-actions on probability spaces, compute them for a class of d-dimensional Markov shifts, and use them to prove that some of these examples are non-isomorphic. The invariants under discussion are of three kinds: the first is associated with the higher-order mixing behaviour of the Z(d)-action, and is related-in this class of examples-to an an arithmetical result by David Masser, the second arises from certain relative entropies associated with the Z(d)-action, and the third is a collection of canonical invariant sigma-algebras. The results of this paper are generalizations of earlier results by Kitchens and Schmidt, and we include a proof of David Masser's unpublished theorem.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Journal or Publication Title:	ERGODIC THEORY AND DYNAMICAL SYSTEMS
Publisher:	CAMBRIDGE UNIV PRESS
ISSN:	0143-3857
Date:	December 1993
Volume:	13
Number:	Part 4
Number of Pages:	31
Page Range:	pp. 705-735
Publication Status:	Published
URI:	http://wrap.warwick.ac.uk/id/eprint/20800

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