Completely degenerate lower-dimensional invariant tori for Hamiltonian system

DOI10.1016/j.jde.2018.12.001zbMath1415.37082OpenAlexW2905442995MaRDI QIDQ1732144

Bin Liu, Shengqing Hu

Publication date: 22 March 2019

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.12.001

zbMATH Keywords

KAM iterationcompletely degenerate Hamiltonian systemlow-dimensional tori

Mathematics Subject Classification ID

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 (15)

Degenerate response tori in Hamiltonian systems with higher zero-average perturbation ⋮ Persistence of degenerate hyperbolic lower-dimensional invariant tori in Hamiltonian systems with Bruno’s conditions ⋮ Response solutions in singularly perturbed, quasi-periodically forced nonlinear oscillators ⋮ Response solutions for degenerate reversible harmonic oscillators with zero-average perturbation ⋮ Response solutions of a class of degenerate quasi-periodic systems with a small parameter ⋮ Persistence of degenerate lower dimensional invariant tori with prescribed frequencies in reversible systems ⋮ Response solutions of degenerate quasi-periodic systems under small perturbations ⋮ Response solutions of 2-dimensional degenerate systems under quasi-periodic perturbations ⋮ Completely degenerate responsive tori in Hamiltonian systems ⋮ Persistence of degenerate lower dimensional invariant tori in reversible systems with Bruno non-degeneracy conditions ⋮ Moser's theorem for hyperbolic-type degenerate lower tori in Hamiltonian system ⋮ Response solutions of 3-dimensional degenerate quasi-periodic systems with small parameter ⋮ Response solutions in degenerate oscillators under degenerate perturbations ⋮ Persistence of lower dimensional degenerate invariant tori with prescribed frequencies in Hamiltonian systems with small parameter ⋮ Persistence of multi-dimensional degenerate hyperbolic lower dimensional invariant tori in reversible systems

Cites Work

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• Construction of response solutions for two classes of quasi-periodically forced four-dimensional nonlinear systems with degenerate equilibrium point under small perturbations
• On elliptic lower dimensional tori in Hamiltonian systems
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• Perturbations of lower dimensional tori for Hamiltonian systems
• Nearly integrable infinite-dimensional Hamiltonian systems
• Degenerate lower-dimensional tori in 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
• Response solutions and quasi-periodic degenerate bifurcations for quasi-periodically forced systems
• On lower dimensional invariant tori in reversible systems

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