Non-degenerate Liouville tori are KAM stable

DOI10.1016/j.aim.2016.01.012zbMath1336.37048arXiv1412.0509OpenAlexW2963159657MaRDI QIDQ5965065

Abed Bounemoura

Publication date: 2 March 2016

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.0509

zbMATH Keywords

Hamiltonian systemsKAM stabilitynon-degenerate Liouville tori

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

Related Items (4)

Generic perturbations of linear integrable Hamiltonian systems ⋮ On the divergence of Birkhoff normal forms ⋮ Hamiltonian and reversible systems with smooth families of invariant tori ⋮ Instabilities of invariant quasi-periodic tori

Cites Work

• Unnamed Item
• Normal forms, stability and splitting of invariant manifolds. I: Gevrey Hamiltonians
• Normal forms, stability and splitting of invariant manifolds. II: Finitely differentiable Hamiltonians
• KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character
• Some open problems in dynamical systems
• Stability and instability for Gevrey quasi-convex near-integrable Hamiltonian systems
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Multivariate simultaneous approximation
• Around the stability of KAM tori
• KAM à la R
• A Diophantine duality applied to the KAM and Nekhoroshev theorems
• Integrability of hamiltonian systems on cantor sets
• Stabilité ou instabilité des points fixes elliptiques
• KAM theorem for Gevrey Hamiltonians

This page was built for publication: Non-degenerate Liouville tori are KAM stable