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Spatial determinism for a free Z2-action

Published online by Cambridge University Press:  16 December 2011

ROBERT BURTON  and
KYEWON K. PARK
ROBERT BURTON
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, OR, USA (email: burton@math.oregonstate.edu)
KYEWON K. PARK
Affiliation:
Department of Mathematics, Ajou University, Suwon 443-749, Korea (email: kkpark@ajou.ac.kr)
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Abstract

We extend the idea of bilateral determinism of a free Z-action by D. Ornstein and B. Weiss to a free Z2-action. We show that we have a ‘stronger’ spatial determinism for Z2-actions: to determine the complete Z2-name of a point, it is enough to know the name of a fraction of the orbit whose density can be made arbitrarily small. Moreover, for zero-entropy Z2-actions, we prove that there exists a partition such that the -names of an arbitrarily small one-sided cone determine the points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 32 , Issue 2: Daniel J. Rudolph – in Memoriam , April 2012 , pp. 479 - 489
Copyright
Copyright © Cambridge University Press 2011

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