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arXiv · 2303.04367

KAM-rigidity for parabolic affine abelian actions

Danijela Damjanovic·Bassam Fayad·Maria Saprykina
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Abstract

We show the following dichotomy for a linear parabolic $\mathbb Z^2$-action $\rho_L$ on the torus with at least one step-2 generator: (i) Any affine $\mathbb Z^2$-action with linear part $\rho_L$ has a $\mathbb Z$-factor that is either identity or genuinely parabolic, and is thus not KAM-rigid, or (ii) Almost every affine $\mathbb Z^2$-action with linear part $\rho_L$ is KAM-rigid under volume preserving perturbations.

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Danijela Damjanovic, Bassam Fayad, Maria Saprykina. 2023-03-08. KAM-rigidity for parabolic affine abelian actions. https://arxiv.org/abs/2303.04367

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