2017/05/19 by Abed Bounemoura, Bounemoura, Abed, Jacques Féjoz +1
Mathematics · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1705.06909
openalex publication_date 2017/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove a new invariant torus theorem, for α-Gevrey smooth Hamiltonian systems, under an arithmetic assumption which we call the α-Bruno-Rüssmann condition, and which reduces to the classical Bruno-Rüssmann condition in the analytic category. Our proof is direct in the sense that, for analytic Hamiltonians, we avoid the use of complex extensions and, for non-analytic Hamiltonians, we do not use analytic approximation nor smoothing operators. Following Bessi, we also show that if a slightly weaker arithmetic condition is not satisfied, the invariant torus may be destroyed. Crucial to this work are new functional estimates in the Gevrey class.