Positive measure of KAM tori for finitely differentiable Hamiltonians

2018/12/07 by Abed Bounemoura, Bounemoura, Abed
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.1812.03067

openalex publication_date 2018/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider an integer n ≥ 2 and real numbers τ>n-1 and l>2(τ+1). Using ideas of Moser, Salamon proved that individual Diophantine tori persist for Hamiltonian systems which are of class C^l. Under the stronger assumption that the system is a C^l+τ perturbation of an analytic integrable system, Pöschel proved the persistence of a set of positive measure of Diophantine tori. We improve the last result by showing it is sufficient for the perturbation to be of class C^l and the integrable part to be of class C^l+2.

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