Invariant tori and Lagrange stability of pendulum-type equations

DOI10.1016/0022-0396(90)90088-7zbMath0702.34047OpenAlexW1988096428MaRDI QIDQ914932

Jiangong You

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0022-0396(90)90088-7

zbMATH Keywords

Lagrange stabilitynon-autonomous pendulum-like equations

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Stability of solutions to ordinary differential equations (34D20) Stability theory for smooth dynamical systems (37C75)

Related Items (24)

Lagrange stability for asymptotic linear Duffing equations ⋮ Boundedness of solutions for non-linear quasi-periodic differential equations with Liouvillean frequency ⋮ Boundedness of solutions for some impulsive pendulum-type equations ⋮ Persistence of invariant tori in integrable Hamiltonian systems under almost periodic perturbations ⋮ Generic existence of invariant Cantori in pendulum-type equations ⋮ Persistence of invariant tori for almost periodically forced reversible systems ⋮ The existence of quasiperiodic solutions for coupled Duffing-type equations ⋮ Boundedness of solutions and existence of invariant tori for a generalized pendulum type equation ⋮ Quasiperiodic solutions for nonlinear differential equations of second order with symmetry ⋮ Aubry-mather theorem and quasiperiodic orbits for time dependent reversible systems ⋮ Complete orbits for twist maps on the plane: extensions and applications ⋮ Relativistic pendulum and invariant curves ⋮ The coexistence of quasi-periodic and blow-up solutions in a class of Hamiltonian systems ⋮ Nonlinear rotations ⋮ Twist Mappings with Non-Periodic Angles ⋮ The parametrically forced pendulum: A case study in \(1\frac12\) degree of freedom ⋮ Unbounded solutions to almost-periodically forced pendulum-type equations ⋮ Quasiperiodic dynamics in Hamiltonian \(1\frac{1}{2}\) degree of freedom systems far from integrability ⋮ Dynamical behaviors for generalized pendulum type equations with \(p\)-Laplacian ⋮ Unnamed Item ⋮ Destruction of invariant tori in pendulum-type equations ⋮ Boundedness of solutions of nonlinear differential equations ⋮ Lagrangian stability of a nonlinear quasi-periodic system ⋮ Kolmogorov stability, the impossibility of Fermi acceleration and the existence of periodic solutions in some Hamiltonian-type systems

Cites Work

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• Multiple solutions of the periodic boundary value problem for some forced pendulum-type equations
• Stable and Random Motions in Dynamical Systems
• A stability theorem for minimal foliations on a torus

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