## Abstract

We obtain general results on the stability of rapid (superpolynomial)
decay of correlations for hyperbolic flows.
Let M be an n-dimensional
compact manifold, r>= 2n-1. Amongst the C^r Axiom A flows, there
is a C^{2n-1}-open, C^r-dense set of flows for which each
nontrivial hyperbolic basic set is rapid mixing.
For nontrivial *attracting* hyperbolic basic sets, we
obtain a C^1-open, C^r-dense set of rapid mixing flows, each r>=1.
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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