JournalsjemsVol. 22, No. 7pp. 2253–2285

Open sets of exponentially mixing Anosov flows

  • Oliver Butterley

    ICTP, Trieste, Italy
  • Khadim War

    Ruhr-Universität Bochum, Germany
Open sets of exponentially mixing Anosov flows cover
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Abstract

We prove that an Anosov flow with C1\mathcal C^1 stable bundle mixes exponentially whenever the stable and unstable bundles are not jointly integrable. This allows us to show that if a flow is sufficiently close to a volume-preserving Anosov flow and dimEs=1\mathbb E_s = 1, dimEu2\mathbb E_u \geq 2 then the flow mixes exponentially whenever the stable and unstable bundles are not jointly integrable. This implies the existence of non-empty open sets of exponentially mixing Anosov flows. As part of the proof of this result we show that C1+\mathcal C^{1+} uniformly expanding suspension semiflows (in any dimension) mix exponentially when the return time is not cohomologous to a piecewise constant.

Cite this article

Oliver Butterley, Khadim War, Open sets of exponentially mixing Anosov flows. J. Eur. Math. Soc. 22 (2020), no. 7, pp. 2253–2285

DOI 10.4171/JEMS/964