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
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
Houston
TX 77005-1892