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