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.
Funding Statement
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.
Citation
Alexander Gorodnik. Ralf Spatzier. "Mixing properties of commuting nilmanifold automorphisms." Acta Math. 215 (1) 127 - 159, 2015. https://doi.org/10.1007/s11511-015-0130-0
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