Abstract
The problem of the stability of an equilibrium position of an autonomous and nonautonomous 2π-periodic Hamiltonian system with n degrees of freedom, in a nonlinear setting, is studied in the presence and absence of resonance. In this work some of the main results concerning to the theory of stability in the Liapunov’s sense of equilibrium points are presented. In general the conditions that assure stability and instability in the sense of Liapunov and formal stability of the equilibrium position are given in function of the coefficients of the Hamiltonian function. Also, we make a complete study of the type of stability of the libration points in the circular restricted three body problem in the planar case. At this point, we reviewed several papers in the literature with these topics.
Published Version
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