  In this paper we study the decay of correlations for Gibbs measures
associated to codimension one Axiom A attractors for flows. We prove that a
codimension one Axiom A attractors whose strong stable foliation is
$C^{1+\alpha}$ either have exponential decay of correlations with respect to
all Gibbs measures associated to H\"older continuous potentials or their stable
and unstable bundles are jointly integrable. As a consequence, there exist
$C^1$-open sets of $C^3$-vector fields generating Axiom A flows having
attractors so that: (i) mix exponentially with respect to equilibrium states
associated with H\"older continuous potentials, (ii) their time-1 maps satisfy
an almost sure invariance principle, and (iii) the growth of the number of
closed orbits of length $T$ is described by the topological entropy of the
attractor.
