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Tiling representations of ${\Bbb R}^{\bf 2}$ actions and $\balpha$-equivalence in two dimensions

Published online by Cambridge University Press:  01 October 1998

AYŞE ARZU ŞAHIN
AYŞE ARZU ŞAHIN
Affiliation:
Department of Mathematics, North Dakota State University, Fargo, ND 58105, USA (e-mail: sahin@plains.nodak.edu)
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Abstract

We study ${\Bbb Z}^2$ actions arising as base point actions of tiling representations of ${\Bbb R}^2$ flows. We cast an equivalence relation between such actions in terms of a simple arithmetic condition on an orbit equivalence. Stated as such, our equivalence class is easily seen to be a restricted even Kakutani equivalence, as we well as a higher-dimensional generalization of $\alpha$-equivalence, defined by Fieldsteel, del Junco and Rudolph for ${\Bbb Z}$ actions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 18 , Issue 5 , October 1998 , pp. 1211 - 1255
Copyright
© 1998 Cambridge University Press

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