Minimal (G, τ)-extensions

Harvey Bayard Keynes and D. Newton

Vol. 77 (1978), No. 1, 145–163

DOI: 10.2140/pjm.1978.77.145

Abstract

In this paper, we are concerned with lifting minimality and topological transitivity through skew-extensions—the fibres being a compact group and the action intertwines with a group automorphism. It is shown that in the class of cocycles respecting the automorphism, these properties can be lifted when the automorphism is distal. This is obtained by a dynamical decomposition of an automorphism on a group, and subsequent analysis based on this decomposition. The lifting fails for hyperbolic automorphisms on a torus.

Mathematical Subject Classification 2000

Primary: 54H20

Milestones

Received: 2 March 1977

Revised: 26 September 1977

Published: 1 July 1978