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Rank one and loosely Bernoulli actions in ${\Bbb Z}^{\bi d}$

Published online by Cambridge University Press:  01 October 1998

AIMEE S. A. JOHNSON  and
AYŞE A. ŞAHİN
AIMEE S. A. JOHNSON
Affiliation:
Department of Mathematics and Statistics, Swarthmore College, Swarthmore, PA 19081, USA (e-mail: aimee@cc.swarthmore.edu)
AYŞE A. ŞAHİN
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, ND 58103, USA (e-mail: sahin@plains.nodak.edu)
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Abstract

We define rank one for ${\Bbb Z}^d$ actions and show that those rank one actions with a certain tower shape are loosely Bernoulli for $d\ge 1$. We also construct a zero entropy ${\Bbb Z}^2$ loosely Bernoulli action with a zero entropy, ergodic, non-loosely Bernoulli one-dimensional subaction.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 5 , October 1998 , pp. 1159 - 1172
Copyright
© 1998 Cambridge University Press

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