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Markov odometer actions not of product type

Published online by Cambridge University Press:  20 June 2003

A. H. DOOLEY  and
T. HAMACHI
A. H. DOOLEY
Affiliation:
School of Mathematics, University of New South Wales, Sydney 2052 NSW, Australia (e-mail: [email protected])
T. HAMACHI
Affiliation:
Graduate School of Mathematics, Kyushu University, Ropponmatsu, Chuo-Ku, Fukuoka 810, Japan
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Abstract

We find an explicit example of a Markov odometer action which is not orbit-equivalent to any product odometer action. We make use of some techniques from Krieger's construction of an action of non-product type arising from a flow. However, his example is not realized as an odometer action with an explicit measure, nor does it arise from a Markov measure.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 23 , Issue 3 , June 2003 , pp. 813 - 829
Copyright
2003 Cambridge University Press

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