English

Mixing Properties of Commuting Nilmanifold Automorphisms

Dynamical Systems 2013-05-10 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1211.0987,
  title  = {Mixing Properties of Commuting Nilmanifold Automorphisms},
  author = {Alexander Gorodnik and Ralf Spatzier},
  journal= {arXiv preprint arXiv:1211.0987},
  year   = {2013}
}