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Mixing properties of commuting nilmanifold automorphisms

Alexander Gorodnik School of Mathematics, University of Bristol Ralf Spatzier Department of Mathematics, University of Michigan

Dynamical Systems mathscidoc:1701.11010

Acta Mathematica, 215, (1), 127-159, 2013.5
We study mixing properties of commutative groups of automorphisms acting on compact nilmanifolds. Assuming that every non-trivial element acts ergodically, we prove that such actions are mixing of all orders. We further show exponential 2-mixing and 3-mixing. As an application we prove smooth cocycle rigidity for higher-rank abelian groups of nilmanifold automorphisms.
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@inproceedings{alexander2013mixing,
  title={Mixing properties of commuting nilmanifold automorphisms},
  author={Alexander Gorodnik, and Ralf Spatzier},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203405437689806},
  booktitle={Acta Mathematica},
  volume={215},
  number={1},
  pages={127-159},
  year={2013},
}
Alexander Gorodnik, and Ralf Spatzier. Mixing properties of commuting nilmanifold automorphisms. 2013. Vol. 215. In Acta Mathematica. pp.127-159. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203405437689806.
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