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$\mathbb{Z}^d$ Staircase actions

Published online by Cambridge University Press:  02 April 2001

TERRENCE ADAMS  and
CESAR E. SILVA
TERRENCE ADAMS
Affiliation:
Department of Mathematics and Computer Science, Rhode Island College, 600 Mount Pleasant Ave., Providence, RI 02908, USA (e-mail: tadams@ric.edu)
CESAR E. SILVA
Affiliation:
Department of Mathematics, Williams College, Williamstown, MA 01267 USA (e-mail: csilva@williams.edu)
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Abstract

We define staircase $\mathbb{Z}^d$ actions. We first prove that staircase $\mathbb{Z}^2$ actions satisfying a general condition are mixing. Then we describe how to extend the results to the staircase $\mathbb{Z}^d$ actions. Thus we have constructed explicitly rank one mixing $\mathbb{Z}^d$ actions which include natural analogues to the well-known staircase transformation.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 4 , August 1999 , pp. 837 - 850
Copyright
1999 Cambridge University Press

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