We extend recent results of Adler, Kitchens & Shub, Parry, and Parry & Pollicott on the stable ergodicity and mixing of toral extensions to skew extensions by compact connected Lie groups. We show that Holder continuous extensions by a compact Lie group over a hyperbolic attractor are generically stably ergodic. If the group is compact semisimple, then Holder continuous extensions over hyperbolic sets are generically stably ergodic.

For preprint, email: mikefield@gmail.com

Professor Mike Field
Department of Mathematics
Imperial College
London SW7 2AZ