Persistence of the non-twist torus in nearly integrable hamiltonian systems

DOI10.1090/S0002-9939-10-10151-8zbMath1202.37079OpenAlexW2078697675MaRDI QIDQ3574813

Junxiang Xu, Jiangong You

Publication date: 2 July 2010

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-10-10151-8

zbMATH Keywords

Hamiltonian systeminvariant toriKAM iterationnon-degeneracy condition

Mathematics Subject Classification ID

Perturbations of ordinary differential equations (34D10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Global stability of solutions to ordinary differential equations (34D23) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)

Related Items (15)

Persistence of invariant tori in infinite-dimensional Hamiltonian systems ⋮ Persistence of lower dimensional hyperbolic tori for reversible system ⋮ General KAM theorems and their applications to invariant tori with prescribed frequencies ⋮ Persistence of invariant tori in integrable Hamiltonian systems under almost periodic perturbations ⋮ 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 ⋮ Invariant tori with prescribed frequency for nearly integrable hamiltonian systems ⋮ Non-Floquet invariant tori in reversible systems ⋮ On the linearization of vector fields on a torus with prescribed frequency ⋮ On invariant tori of nearly integrable Hamiltonian systems with quasiperiodic perturbation ⋮ Existence of invariant curves with prescribed frequency for degenerate area preserving mappings ⋮ Persistence of hyperbolic-type degenerate lower-dimensional invariant tori with prescribed frequencies in Hamiltonian systems ⋮ A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems ⋮ Existence of invariant curves for area-preserving mappings under weaker non-degeneracy conditions ⋮ THE ISOENERGETIC KAM-TYPE THEOREM AT RESONANT CASE fOR NEARLY INTEGRABLE HAMILTONIAN SYSTEMS

Cites Work

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• 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
• Invariant tori in non-degenerate nearly integrable Hamiltonian systems
• Birkhoff-Kolmogorov-Arnold-Moser tori in convex Hamiltonian systems
• KAM-stable Hamiltonians
• Convergent series expansions for quasi-periodic motions
• Integrability of hamiltonian systems on cantor sets
• Analytic Extensions of Differentiable Functions Defined in Closed Sets
• Unfoldings and bifurcations of quasi-periodic tori

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