Mixing properties of commuting nilmanifold automorphisms

• 成果类型: Article
• 署名作者: Gorodnik, Alexander; Spatzier, Ralf
• 署名单位: University of Bristol; University of Bristol; University of Michigan System; University of Michigan
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-015-0130-0
• 发表日期: 2015
• 页码: 127-159
• 关键词: anosov actions; compact-groups; RIGIDITY; EQUATIONS; THEOREM; lie

摘要

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.