a1 Department of Mathematics, Oregon State University, Corvallis, OR, USA (email: firstname.lastname@example.org)
a2 Department of Mathematics, Ajou University, Suwon 443-749, Korea (email: email@example.com)
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.
(Received December 31 2010)
(Revised August 19 2011)
(Online publication December 16 2011)