Ergodic Theory and Dynamical Systems

Research Article

Restricted orbit changes of ergodic ℤd-actions to achieve mixing and completely positive entropy

Adam Fieldsteela1 and N. A. Friedmana2

a1 Department of Mathematics, Wesleyan University, Middletown, CT 06457, USA;

a2 Department of Mathematics and Statistics, State University of New York, Albany, NY 12222, USA

Abstract

We show that for every ergodic ℤd-action T, there is a mixing ℤd-action S which is orbit equivalent to T via an orbit equivalence that is a weak a-equivalence for all a ≥ 1 and a strong b-equivalence for all b (0, 1). If T has positive entropy, then S can be taken to have completely positive entropy. If the dimension d is greater than one, the orbit equivalence may be taken to be bounded and a strong b-equivalence for all b > 0.

(Received April 17 1984)

(Revised November 19 1985)