Mixing properties of commuting nilmanifold automorphisms

Alexander Gorodnik*, Ralf Spatzier

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)127-159
Number of pages33
JournalActa Mathematica
Volume215
Issue number1
DOIs
Publication statusPublished - 1 Sep 2015

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