Decay of correlations for certain isometric extensions of Anosov flows

We 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.

Automated summary

This paper establishes 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 achieved by translating the accessibility properties of the extension into local non-integrability estimates measured by infinitesimal transitivity groups, which allows us to obtain contraction properties for a class of 'twisted' symbolic transfer operators.