Speedups of ergodic group extensions
by
Adam Fieldsteel
Wesleyan University
Coauthors: Andrey Babichev, Cal State Fresno

A speedup of a finite measure preserving transformation T is a transformation of the form T^k(x), where k(x) is a measurable function taking values in the natural numbers. A theorem of Arnoux, Ornstein and Weiss says that if T is ergodic, then every ergodic S is obtainable (up to isomorphism) as a speedup of T. We obtain a conditional version of this result, applied to ergodic extensions of transformations by rotations of a compact group. Specifically, Given any two such extensions U and V, there is a speedup U^k(x) of U, where the variable exponent k is constant on group fibers, so that U^k(x) is isomorphic to V, and where the isomorphism also preserves the fibers and acts by rotation on them.

The methods give a new proof of the earlier result, and are related to the general notion of restricted orbit equivalence.

Date received: March 28, 2008