Stability of equilibrium solutions of autonomous and periodic Hamiltonian systems with \(n\)-degrees of freedom in the case of single resonance

DOI10.1007/S10884-010-9176-ZzbMath1209.37026OpenAlexW2085438912MaRDI QIDQ616203

Fabio dos Santos, José Edmundo Mansilla, Claudio Vidal

Publication date: 7 January 2011

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

Full work available at URL: https://doi.org/10.1007/s10884-010-9176-z

zbMATH Keywords

stabilityHamiltonian systemresonanceperiodicautonomous

Mathematics Subject Classification ID

Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Stability of solutions to ordinary differential equations (34D20) Stability theory for smooth dynamical systems (37C75)

Related Items (12)

The linearization of periodic Hamiltonian systems with one degree of freedom under the Diophantine condition ⋮ Nonlinear stability of elliptic equilibria in Hamiltonian systems with resonances of order four with interactions ⋮ Normal stability of autonomous and periodic linear Hamiltonian systems ⋮ Stability of the equilibrium solutions in a charged restricted circular three-body problem ⋮ Nonlinear stability of elliptic equilibria in Hamiltonian systems with exponential time estimates ⋮ On the nonlinear stability of the triangular points in the circular spatial restricted three-body problem ⋮ Nonlinear Stability in the Spatial Attitude Motion of a Satellite in a Circular Orbit ⋮ Stability of equilibrium solutions of Hamiltonian systems with \(n\)-degrees of freedom and single resonance in the critical case ⋮ Asymptotic stability estimates near an equilibrium point ⋮ Stability of the polar equilibria in a restricted three-body problem on the sphere ⋮ Instability of equilibrium solutions of Hamiltonian systems with \(n\)-degrees of freedom under the existence of a single resonance and an invariant ray ⋮ Stability of equilibrium solutions of autonomous and periodic Hamiltonian systems in the case of multiple resonances

Cites Work

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• The stability of the Lagrange triangular point and a theorem of Arnold
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• PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIAN
• Third and fourth order resonances in Hamiltonian systems
• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem
• Nonlinear stability in resonant cases: A geometrical approach

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