KAM-tori near an analytic elliptic fixed point

DOI10.1134/S1560354713060154zbMath1417.37212arXiv1401.5748MaRDI QIDQ2449302

Raphaël Krikorian, Bassam Fayad, L. Hakan Eliasson

Publication date: 7 May 2014

Published in: Regular and Chaotic Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.5748

zbMATH Keywords

stabilitynormal formsKAM theoryHamiltonian dynamicsinvariant torielliptic fixed pointsHerman's conjectureRussmann's condition

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) Stability problems for problems in Hamiltonian and Lagrangian mechanics (70H14) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (11)

Lyapunov unstable elliptic equilibria ⋮ On the divergence of Birkhoff normal forms ⋮ Almost periodic invariant tori for the NLS on the circle ⋮ Elliptic Bubbles in Moser's 4D Quadratic Map: The Quadfurcation ⋮ A formal KAM theorem for Hamiltonian systems and its application to hyperbolic lower dimensional invariant tori ⋮ Isolated elliptic fixed points for smooth Hamiltonians ⋮ Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems ⋮ Moser's quadratic, symplectic map ⋮ Super-exponential stability for generic real-analytic elliptic equilibrium points ⋮ Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter ⋮ Convergence of the Birkhoff normal form sometimes implies convergence of a normalizing transformation

Cites Work

• A KAM phenomenon for singular holomorphic vector fields
• Some open problems in dynamical systems
• KAM-stable Hamiltonians
• Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung

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