STABLE ERGODICITY OF SKEW EXTENSIONS BY COMPACT LIE GROUPS

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 Hِlder continuous extensions by a compact Lie group over a hyperbolic attractor are generically stably ergodic. If the group is compact semisimple, then Hِlder continuous extensions over hyperbolic sets are generically stably ergodic.