Degenerate lower dimensional invariant tori in reversible system

DOI10.3934/DCDS.2018162zbMath1409.37062OpenAlexW2807646305MaRDI QIDQ1661138

Shengqing Hu, Bin Liu

Publication date: 16 August 2018

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2018162

zbMATH Keywords

reversible systemsinvariant toriKAM iteration

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 (10)

Persistence of invariant tori for almost periodically forced reversible systems ⋮ Response solutions in singularly perturbed, quasi-periodically forced nonlinear oscillators ⋮ Response solutions for degenerate reversible harmonic oscillators with zero-average perturbation ⋮ Persistence of degenerate lower dimensional invariant tori in reversible systems with Bruno non-degeneracy conditions ⋮ On the persistence of lower-dimensional tori in reversible systems with hyperbolic-type degenerate equilibrium point under small perturbations ⋮ Quasi-periodic solutions for a completely resonant beam equation with a nonlinear term depending on the time and space variables ⋮ Response solutions of 3-dimensional degenerate quasi-periodic systems with small parameter ⋮ Response solutions in degenerate oscillators under degenerate perturbations ⋮ Completely degenerate lower-dimensional invariant tori in reversible systems ⋮ Persistence of multi-dimensional degenerate hyperbolic lower dimensional invariant tori in reversible systems

Cites Work

• Unnamed Item
• Unnamed Item
• On small perturbation of two-dimensional quasi-periodic systems with hyperbolic-type degenerate equilibrium point
• Degenerate lower dimensional tori in reversible systems
• Invariant m-dimensional tori of reversible systems with phase space of dimension greater than 2m
• Reversible systems
• A KAM theorem for hyperbolic-type degenerate lower dimensional tori in Hamiltonian systems
• Perturbations of lower dimensional tori for Hamiltonian systems
• Unfoldings of quasi-periodic tori in reversible systems
• Convergent series expansions for quasi-periodic motions
• On the conservation of hyperbolic invariant tori for Hamiltonian systems
• Quasi-periodic motions in families of dynamical systems. Order amidst chaos
• On the persistence of degenerate lower-dimensional tori in reversible systems
• The iteration-approximation decoupling in the reversible KAM theory
• Partial preservation of frequencies in KAM theory
• On lower dimensional invariant tori in reversible systems

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