Open sets of exponentially mixing Anosov flows

  • Oliver Butterley

    ICTP, Trieste, Italy
  • Khadim War

    Ruhr-Universität Bochum, Germany
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Abstract

We prove that an Anosov flow with 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 dim, dim 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 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