Ergodicity in affine skew-product toral extensions

Harvey Bayard Keynes and Mahesh Nerurkar

Vol. 123 (1986), No. 1, 115–126

DOI: 10.2140/pjm.1986.123.115

Abstract

We examine the dynamics of those skew-product extensions in which the fibre is a torus supporting a group of automorphisms which intertwine with the given Zⁿ action. The main results concern lifting ergodicity generically from the base when the original action is perturbed into new action by a continuous affine cocyle. Extensions are indicated for other properties, such as weak-mixing and Bernoulli, and smooth variants are stated.

Mathematical Subject Classification 2000

Primary: 28D05

Secondary: 54H20, 58F11

Milestones

Received: 15 October 1984

Revised: 16 May 1985

Published: 1 May 1986