On singular Hamiltonians: the existence of quasi-periodic solutions and nonlinear stability

DOI10.1090/S0273-0979-1989-15689-9zbMath0699.34042MaRDI QIDQ3477182

Chjan C. Lim

Publication date: 1989

Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Hamiltonian systemsN-body problems of celestial mechanicsstar dynamics

Mathematics Subject Classification ID

Vortex flows for incompressible inviscid fluids (76B47) Hamilton's equations (70H05) Complex behavior and chaotic systems of ordinary differential equations (34C28) (n)-body problems (70F10) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Stability theory for ordinary differential equations (34D99)

Related Items (4)

Chaotic motion of the \(N\)-vortex problem on a sphere. I. Saddle-centers in two-degree-of-freedom Hamiltonians ⋮ Quasi-periodic dynamics of desingularized vortex models ⋮ Binary trees, symplectic matrices and the Jacobi coordinates of celestial mechanics ⋮ Calculus of variations and optimal control for generalized functions

Cites Work

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• The stability of the Lagrange triangular point and a theorem of Arnold
• Singular manifolds and quasi-periodic solutions of Hamiltonians for vortex lattices
• Quasi-periodic dynamics of desingularized vortex models
• Stable and Random Motions in Dynamical Systems
• Nonexistence of Lyapunov functions and the instability of the von Kármán vortex streets
• On some new long periodic solutions of the plane restricted three body problem
• Regularization of kepler's problem and the averaging method on a manifold

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