KAM-rigidity for parabolic affine abelian actions

2023/03/08 by Danijela Damjanović, Damjanovic, Danijela, Bassam Fayad +3
Mathematics · Physics and Astronomy · #37C15 #37C85 #37D30 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2303.04367

openalex publication_date 2023/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show the following dichotomy for a linear parabolic \mathbb Z²-action ρ_L on the torus with at least one step-2 generator: (i) Any affine \mathbb Z²-action with linear part ρ_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 Z²-action with linear part ρ_L is KAM-rigid under volume preserving perturbations.

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