A KAM theorem for reversible systems of infinite dimension

DOI10.1007/s10114-005-0887-8zbMath1129.37043OpenAlexW2089461800MaRDI QIDQ2465534

Shun Qing Chen, Xiao Ping Yuan

Publication date: 4 January 2008

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-005-0887-8

zbMATH Keywords

periodic solutionsfrictionKAM theoremweakly coupled oscillatorsreversible system

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55)

Related Items (4)

Whitney smooth families of invariant tori within the reversible context 2 of KAM theory ⋮ Quasi-periodic solutions for the reversible derivative nonlinear Schrödinger equations with periodic boundary conditions ⋮ On the Kolmogorov theorem for some infinite-dimensional Hamiltonian systems of short range ⋮ Construction of invariant whiskered tori by a parameterization method. II: Quasi-periodic and almost periodic breathers in coupled map lattices

Cites Work

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• Quasi-periodic solutions of completely resonant nonlinear wave equations
• Small divisors with spatial structure in infinite dimensional Hamiltonian systems
• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory
• Localization in disordered, nonlinear dynamical systems
• Reversible systems
• Boundedness of solutions of nonlinear differential equations
• Nearly integrable infinite-dimensional Hamiltonian systems
• Construction of quasi-periodic breathers via KAM technique
• Existence of invariant tori for certain weakly reversible mappings
• Stable and Random Motions in Dynamical Systems
• Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators
• Quasiperiodic solutions and boundedness of solutions for a class of nonlinear differential equations of second order
• Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators
• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN

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