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ON THE EXISTENCE OF MARKOV PARTITIONS FOR ${\mathbb Z}^{\lowercase{d}}$ ACTIONS

Published online by Cambridge University Press:  24 May 2004

E. ARTHUR ROBINSON JR  and
AYŞE A. ŞAHİN
E. ARTHUR ROBINSON JR
Affiliation:
Department of Mathematics, George Washington University, Washington DC 20052, USArobinson@gwu.edu
AYŞE A. ŞAHİN
Affiliation:
Department of Mathematical Sciences, DePaul University, 2320 North Kenmore Avenue, Chicago, IL 60614-7807, USAasahin@condor.depaul.edu
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Abstract

The theory of higher-dimensional shifts of finite type is still largely an open area of investigation. Recent years have seen much activity, but fundamental questions remain unanswered. In this paper we consider the following basic question. Given a shift of finite type (SFT), under what topological mixing conditions are we guaranteed the existence of Bernoulli (or even $K$, mixing, or weakly mixing) invariant measures?

Keywords

37B50
Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 69 , Issue 3 , June 2004 , pp. 693 - 706
Copyright
The London Mathematical Society 2004

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