KAM rigidity for partially hyperbolic affine Z^k actions on the torus with a rank one factor

Danijela Damjanovic; Bassam Fayad

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arXiv · 1308.3546

KAM rigidity for partially hyperbolic affine Z^k actions on the torus with a rank one factor

Danijela Damjanovic·Bassam Fayad

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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.

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Danijela Damjanovic, Bassam Fayad. 2013-08-16. KAM rigidity for partially hyperbolic affine Z^k actions on the torus with a rank one factor. https://arxiv.org/abs/1308.3546

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