Decay of correlations for certain isometric extensions of Anosov flows

Abstract

AbstractWe establish exponential decay of correlations of all orders for locally G-accessible isometric extensions of transitive Anosov flows, under the assumption that the strong stable and strong unstable distributions of the base Anosov flow are  $C^1$ . This is accomplished by translating accessibility properties of the extension into local non-integrability estimates measured by infinitesimal transitivity groups used by Dolgopyat, from which we obtain contraction properties for a class of ‘twisted’ symbolic transfer operators.