Exponential Mixing of Nilmanifold Automorphisms
Dynamical Systems
2012-10-09 v1
Abstract
We study dynamical properties of automorphisms of compact nilmanifolds and prove that every ergodic automorphism is exponentially mixing and exponentially mixing of higher orders. This allows to establish probabilistic limit theorems and regularity of solutions of the cohomological equation for such automorphisms. Our method is based on the quantitative equidistribution results for polynomial maps combined with Diophantine estimates.
Cite
@article{arxiv.1210.2271,
title = {Exponential Mixing of Nilmanifold Automorphisms},
author = {Alexander Gorodnik and Ralf Spatzier},
journal= {arXiv preprint arXiv:1210.2271},
year = {2012}
}