Mixing properties of commuting nilmanifold automorphisms. (English) Zbl 1360.37010
Summary: 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.
MSC:
| 37A25 | Ergodicity, mixing, rates of mixing |
| 22D40 | Ergodic theory on groups |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
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