Ergodic continuous skew product actions of amenable groups

Mahesh Nerurkar

Vol. 119 (1985), No. 2, 343–363

DOI: 10.2140/pjm.1985.119.343

Abstract

Given two compact, metric topological dynamical systems (Y,T,μ) and (Z,G,ν), where T and G are locally compact separable groups acting continuously on spaces, preserving finite ergodic measures μ and ν respectively, a continuous cocycle α on (Y,T,μ) defines a skew product T action on Z × Y by (z,y) ⋅ t → (zα(y,t),y ⋅ t). We prove that for a large class of amenable groups T and, under some very general conditions on spaces Y , Z and G, residually many continuous cocycles lift various ergodic and mixing properties from Y to Z × Y . Similar results are obtained for non-trivial compact group extensions of (Y,T,μ).

Mathematical Subject Classification 2000

Primary: 28D15

Secondary: 28A51

Milestones

Received: 29 July 1983

Revised: 2 March 1984

Published: 1 October 1985