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Mixing properties of commuting nilmanifold automorphisms

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Acta Mathematica

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Abstract

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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Authors and Affiliations

  1. School of Mathematics, University of Bristol, Howard House, Queens Ave., Clifton, Bristol, BS8 1SD, U.K

    Alexander Gorodnik

  2. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, U.S.A

    Ralf Spatzier

Authors
  1. Alexander Gorodnik
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  2. Ralf Spatzier
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Corresponding author

Correspondence to Alexander Gorodnik.

Additional information

A. G. was supported in part by EPSRC grant EP/H000091/1 and ERC grant 239606. R. S. was supported in part by NSF grant DMS-0906085.

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Gorodnik, A., Spatzier, R. Mixing properties of commuting nilmanifold automorphisms. Acta Math 215, 127–159 (2015). https://doi.org/10.1007/s11511-015-0130-0

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  • DOI: https://doi.org/10.1007/s11511-015-0130-0

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