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, e-mail: mikefield@gmail.com or Michael.J.Field@rice.edu

Professor Mike Field
Department of Mathematics
Rice University
6100 S Main St
TX 77005-1892