Stable ergodicity and frame flows

Authors: Keith Burns and Mark Pollicott

Abstract:
In this note we show that all diffeomorphisms close enough to the time-one map of the frame flow on certain negatively curved manifolds are ergodic. As a simple corollary we deduce that the frame flows are ergodic for all compact manifolds with curvature pinched sufficiently close to -1, thus providing results in the case of manifolds of dimension 7 or 8 which were missing from the results of Brin and Karcher.

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Two problems related to this paper are included in the Bloomington Geometry Problem List.

Authors' addresses:
	Keith  Burns 
	Department of Mathematics
	Northwestern University
	Evanston, IL 60208-2730
        
        Mark Pollicott
        Mathematics Institute
        University of Warwick
        Coventry CV4 7AL 
        UK