2012/11/05 by Alexander Gorodnik, Ralf Spatzier, Gorodnik, Alexander +1
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals #math.DS
paper · pdf · doi:10.48550/arxiv.1211.0987
openalex publication_date 2012/11/05 · arxiv created 2013/05/09 · arxiv updated 2013/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study mixing properties of commutative groups of automorphisms acting on compact nilmanifolds. Assuming that every nontrivial 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.