Decay of correlations for certain isometric extensions of Anosov flows

Salman Siddiqi

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arXiv · 1908.08550

Decay of correlations for certain isometric extensions of Anosov flows

Salman Siddiqi

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Abstract

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 foliations of the base Anosov flow are jointly $C^1$. This is accomplished by translating accessibility properties of the extension into local non-integrability estimates measured by Dolgopyat's infinitesimal transitivity group, from which we obtain contraction properties for a class of 'twisted' symbolic transfer operators.

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Salman Siddiqi. 2019-08-22. Decay of correlations for certain isometric extensions of Anosov flows. https://arxiv.org/abs/1908.08550

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