On decay of correlations in Anosov flows

  title={On decay of correlations in Anosov flows},
  author={Dmitry Dolgopyat},
  journal={Annals of Mathematics},
  • D. Dolgopyat
  • Published 1 March 1998
  • Mathematics
  • Annals of Mathematics
There is some disagreement about the meaning of the phrase 'chaotic flow.' However, there is no doubt that mixing Anosov flows provides an example of such systems. Anosov systems were introduced and extensively studied in his classical memoir ([A]). Among other things he proved the following fact known now as Anosov alternative for flows: Either every strong stable and strong unstable manifold is everywhere dense or the flow gt is a suspension over an Anosov diffeomorphism by a constant roof… 
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*Dedicated to Micheline Ishay I would like to thank P. Boyland, L. Chierchia, V. Donnay, G. De Martino, C. Gole, J. L. Lebowitz, M. Lyubich, M. Rychlik, I. G. Schwarz, S. Vaienti and especially G.
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