Abstract
We consider the problem of stability of equilibrium points in Hamiltonian systems of two degrees of freedom under resonances. Determining the stability or instability is based on a geometrical criterion based on how two surfaces, related with the normal form, intersect one another. The equivalence of this criterion with a result of Cabral and Meyer is proved. With this geometrical procedure, the hypothesis may be extended to more general cases.
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Elipe, A., Lanchares, V. & Pascual, A. On the Stability of Equilibria in Two-Degrees-of- Freedom Hamiltonian Systems Under Resonances. J Nonlinear Sci 15, 305–319 (2005). https://doi.org/10.1007/s00332-004-0674-1
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DOI: https://doi.org/10.1007/s00332-004-0674-1