KAM rigidity for partially hyperbolic affine Z^k actions on the torus with a rank one factor
Dynamical Systems
2013-08-19 v1
Abstract
We show that ergodic affine abelian discrete actions on the torus, that have a rank-one factor in their linear part, are locally rigid in a KAM sense if and only if the rank one factor is trivial and the action is higher-rank transversally to this factor. Since it has been proved by Damjanovic and Katok that affine actions with higher-rank linear part are locally rigid, our result completes the local rigidity picture for affine actions on the torus.
Keywords
Cite
@article{arxiv.1308.3546,
title = {KAM rigidity for partially hyperbolic affine Z^k actions on the torus with a rank one factor},
author = {Danijela Damjanovic and Bassam Fayad},
journal= {arXiv preprint arXiv:1308.3546},
year = {2013}
}