Persistence of elliptic lower dimensional invariant tori for small perturbation of degenerate integrable Hamiltonian systems

DOI10.1006/JMAA.1997.5313zbMath0889.58045OpenAlexW2045971694MaRDI QIDQ1359581

Junxiang Xu

Publication date: 18 February 1998

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5313

zbMATH Keywords

perturbationinvariant toridegenerate integrable Hamiltonian system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Perturbations of ordinary differential equations (34D10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Ordinary differential equations and systems on manifolds (34C40)

Related Items (6)

Persistence of the hyperbolic lower dimensional non-twist invariant torus in a class of Hamiltonian systems ⋮ Non-Floquet invariant tori in reversible systems ⋮ Unnamed Item ⋮ Non-degeneracy conditions in KAM theory ⋮ Persistence of lower dimensional invariant tori for nearly integrable Hamiltonian systems ⋮ Persistence of lower-dimensional tori under the first Melnikov's non-resonance condition

Cites Work

• On elliptic lower dimensional tori in Hamiltonian systems
• Nearly integrable infinite-dimensional Hamiltonian systems
• Existence of KAM tori in degenerate Hamiltonian systems
• Convergent series expansions for quasi-periodic motions
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Generalized implicit function theorems with applications to some small divisor problems, II
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Unnamed Item
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