Journal of the London Mathematical Society



Notes and Papers

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


E. ARTHUR ROBINSON JR a1 and AYSE A. SAHIN a2
a1 Department of Mathematics, George Washington University, Washington DC 20052, USA robinson@gwu.edu
a2 Department of Mathematical Sciences, DePaul University, 2320 North Kenmore Avenue, Chicago, IL 60614-7807, USA asahin@condor.depaul.edu

Article author query
robinson jr e   [Google Scholar] 
sahin a   [Google Scholar] 
 

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?

(Received September 27 2002)
(Revised July 4 2003)

Maths Classification

37B50.