Quasiperiodic solutions of higher dimensional Duffing's equations via the KAM theorem.

DOI10.1007/BF02876711zbMath1186.37070MaRDI QIDQ1609674

Fubao Zhang

Publication date: 15 August 2002

Published in: Science in China. Series A (Search for Journal in Brave)

zbMATH Keywords

KAM theoremquasiperiodic solutionssymplectic mappinginvariant 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 (3)

The existence of quasiperiodic solutions for coupled Duffing-type equations ⋮ The KAM theorem with a large perturbation and application to the network of Duffing oscillators ⋮ The coexistence of quasi-periodic and blow-up solutions in a class of Hamiltonian systems

Cites Work

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• On elliptic lower dimensional tori in Hamiltonian systems
• Boundedness for solutions of nonlinear Hill's equations with periodic forcing terms via Moser's twist theorem
• Critical point theory and Hamiltonian systems
• Boundedness for solutions of superlinear Duffing equations via the twist theorem
• Boundedness of solutions for semilinear Duffing equations
• Invariant tori of Duffing-type equations
• A note on the KAM theorem for symplectic mappings
• Unboundedness in a Duffing equation with polynomial potentials
• A case of boundedness in Littlewood's problem on oscillatory differential equations
• Periodic solutions of hamiltonian systems
• Existence of quasiperiodic solutions and Littlewood’s boundedness problem of Duffing equations with subquadratic potentials

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