KAM-rigidity for parabolic affine abelian actions

Danijela Damjanovic, Bassam Fayad, Maria Saprykina

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 p…