Stability of rapid mixing (joint with M. Field and I. Melbourne)
Abstract. We obtain general results on the stability of rapid
(superpolynomial) decay of correlations for hyperbolic flows:
amongst the 
Axiom A flows, there is a 
-open,
-dense set
of flows for which each nontrivial hyperbolic basic set is rapid
mixing.
For nontrivial attracting hyperbolic basic sets, we obtain a
-open,
-dense set of rapid mixing flows.
These are consequences of a technique used to prove stable ergodicity of group extensions, and the characterization of rapid mixing flows by Dolgopyat.