On invariant tori of vector field under weaker non-degeneracy condition

DOI10.1007/S00030-015-0326-1zbMath1358.37101OpenAlexW2266880632MaRDI QIDQ745911

Junxiang Xu, Dongfeng Zhang

Publication date: 15 October 2015

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-015-0326-1

zbMATH Keywords

invariant toriKAM iterationsmall divisorsnondegeneracy condition

Mathematics Subject Classification ID

Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Nearly integrable Hamiltonian systems, KAM theory (70H08)

Related Items (9)

Persistence of the hyperbolic lower dimensional non-twist invariant torus in a class of Hamiltonian systems ⋮ On invariant tori with prescribed frequency in Hamiltonian systems ⋮ Reducibility of three dimensional skew symmetric system with Liouvillean basic frequencies ⋮ On the linearization of vector fields on a torus with prescribed frequency ⋮ Existence of invariant curves with prescribed frequency for degenerate area preserving mappings ⋮ On multiplicity and concentration of solutions for a gauged nonlinear Schrödinger equation ⋮ Linearization of a quasi-periodically forced flow on 𝕋^m under Brjuno–Rüssmann non-resonant condition ⋮ On the reducibility of linear quasi-periodic systems with Liouvillean basic frequencies and multiple eigenvalues ⋮ Reducibility of a class of nonlinear quasi-periodic systems with Liouvillean basic frequencies

Cites Work

• KAM iteration with nearly infinitely small steps in dynamical systems of polynomial character
• Gevrey-smoothness of elliptic lower-dimensional invariant tori in Hamiltonian systems under Rüssmann's non-degeneracy condition
• On elliptic lower dimensional tori for Gevrey-smooth Hamiltonian systems under Rüssmann's non-degeneracy condition
• Gevrey-smoothness of invariant tori for analytic nearly integrable Hamiltonian systems under Rüssmann's non-degeneracy condition
• Invariant tori for nearly integrable Hamiltonian systems with degeneracy
• KAM à la R
• A lecture on the classical KAM theorem

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