On lower dimensional invariant tori in reversible systems

DOI10.1006/jdeq.2000.3960zbMath1070.37045OpenAlexW2033862086MaRDI QIDQ5955607

Bin Liu

Publication date: 2001

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

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3960

zbMATH Keywords

persistenceanalyticitytorireversible system

Mathematics Subject Classification ID

Related Items (33)

Whitney smooth families of invariant tori within the reversible context 2 of KAM theory ⋮ Persistence of lower dimensional hyperbolic tori for reversible system ⋮ A new KAM theorem for the hyperbolic lower dimensional tori in reversible systems ⋮ A new KAM iteration with nearly infinitely small steps in reversible systems of polynomial character ⋮ On the persistence of degenerate lower-dimensional tori in reversible systems ⋮ Non-Floquet invariant tori in reversible systems ⋮ Degenerate lower dimensional invariant tori in reversible system ⋮ Unnamed Item ⋮ Persistence of invariant tori for almost periodically forced reversible systems ⋮ Persistence of multiscale degenerate invariant tori for reversible systems with multiscale degenerate equilibrium points ⋮ Persistence of degenerate lower dimensional invariant tori with prescribed frequencies in reversible systems ⋮ The persistence of degenerate lower-dimensional tori in reversible systems with a degenerate normal equilibrium point ⋮ The reversible context 2 in KAM theory: the first steps ⋮ Persistence of lower dimensional tori for a class of nearly integrable reversible systems ⋮ Families of invariant tori in KAM theory: interplay of integer characteristics ⋮ Persistence of lower dimensional invariant tori in a class of reversible systems ⋮ Quasi-periodic perturbations within the reversible context 2 in KAM theory ⋮ Degenerate lower dimensional tori in reversible systems ⋮ Persistence of degenerate lower dimensional invariant tori in reversible systems with Bruno non-degeneracy conditions ⋮ Quasi-periodic solutions with prescribed frequency in reversible systems ⋮ Completely degenerate lower-dimensional invariant tori for Hamiltonian system ⋮ On the persistence of lower-dimensional tori in reversible systems with hyperbolic-type degenerate equilibrium point under small perturbations ⋮ On lower dimensional invariant tori in \(C^d\) reversible systems ⋮ A KAM theorem for the elliptic lower dimensional tori with one normal frequency in reversible systems ⋮ Lower dimensional invariant tori with prescribed frequency for the nonlinear Schrödinger equation ⋮ Degenerate lower-dimensional tori in Hamiltonian systems ⋮ Invariant tori for the Schrödinger equation in the Heisenberg Ferromagnetic chain ⋮ On the persistence of lower-dimensional tori in reversible systems with high dimensional degenerate equilibrium under small perturbations ⋮ Persistence of Floquet invariant tori for a class of non-conservative dynamical systems ⋮ Completely degenerate lower-dimensional invariant tori in reversible systems ⋮ Persistence of multi-dimensional degenerate hyperbolic lower dimensional invariant tori in reversible systems ⋮ Melnikov-type theorem for time reversible system ⋮ On the persistence of lower-dimensional elliptic tori with prescribed frequencies in reversible systems

Cites Work

• Unnamed Item
• Invariant m-dimensional tori of reversible systems with phase space of dimension greater than 2m
• Reversible systems
• On elliptic lower dimensional tori in Hamiltonian systems
• Perturbations of lower dimensional tori for Hamiltonian systems
• Nearly integrable infinite-dimensional Hamiltonian systems
• KAM theory near multiplicity one resonant surfaces in perturbations of a-priori stable Hamiltonian systems
• Invariant tori for nearly integrable Hamiltonian systems with degeneracy
• KAM-type theorem on resonant surfaces for nearly integrable Hamiltonian systems
• Birkhoff-Kolmogorov-Arnold-Moser tori in convex 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, I
• The iteration-approximation decoupling in the reversible KAM theory

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