Instability of equilibrium solutions of Hamiltonian systems with \(n\)-degrees of freedom under the existence of multiple resonances and an application to the spatial satellite problem

DOI10.1007/S10884-018-9679-6zbMath1415.37078OpenAlexW2808181960MaRDI QIDQ2419935

Daniela Cárcamo-Díaz, Claudio Vidal

Publication date: 4 June 2019

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

Full work available at URL: https://doi.org/10.1007/s10884-018-9679-6

zbMATH Keywords

stabilityHamiltonian systemequilibrium solutionmultiple resonanceChetaev's theoreminvariant ray solutionLie normal form

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) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Dynamical systems in classical and celestial mechanics (37N05) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)

Related Items (2)

Nonlinear stability of elliptic equilibria in Hamiltonian systems with resonances of order four with interactions ⋮ Nonlinear stability of elliptic equilibria in Hamiltonian systems with exponential time estimates

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