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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Professor Mike Field
Department of Mathematics
Rice University
6100 S Main St
TX 77005-1892