Speedups of ergodic group extensions

TL;DR

This paper establishes conditions under which ergodic group extensions can be speeded up and made relatively isomorphic, advancing the understanding of their structural relationships in ergodic theory.

Contribution

It proves that all ergodic extensions by a locally compact second countable group can be speeded up to be relatively isomorphic to any given aperiodic extension, providing a new classification tool.

Findings

Existence of a relative speedup for ergodic group extensions

Necessary and sufficient conditions for ergodic n-point or countable extensions to be related

Application of the result to classify ergodic extensions

Abstract

We prove that for all ergodic extensions S_1 of a transformation by a locally compact second countable group G, and for all G-extensions S_2 of an aperiodic transformation, there is a relative speedup of S_1 that is relatively isomorphic to S_2. We apply this result to give necessary and sufficient conditions for two ergodic n-point or countable extensions to be related in this way.