Acta Mathematica

Mixing properties of commuting nilmanifold automorphisms

Alexander Gorodnik and Ralf Spatzier

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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.


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.

Article information

Acta Math., Volume 215, Number 1 (2015), 127-159.

Received: 9 May 2013
Revised: 11 July 2014
First available in Project Euclid: 30 January 2017

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2015 © Institut Mittag-Leffler


Gorodnik, Alexander; Spatzier, Ralf. Mixing properties of commuting nilmanifold automorphisms. Acta Math. 215 (2015), no. 1, 127--159. doi:10.1007/s11511-015-0130-0.

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