Vol. 77, No. 1, 1978

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Minimal (G, τ)-extensions

Harvey Bayard Keynes and D. Newton

Vol. 77 (1978), No. 1, 145–163
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
Authors
Harvey Bayard Keynes
D. Newton