Some general observations about stability of periodic solutions of Hamiltonian systems are presented as well as stability results for the periodic solutions that exist near a collision of pure imaginary eigenvalues. Let I = closed-intergral pdq be the action functional for a periodic orbit. The stability theory is based on the surprising result that changes in stability are associated with changes in the sign of dI/d-omega, where omega is the frequency of the periodic orbit. A stability index based on dI/d-omega is defined and rigorously justified using Floquet theory and complete results for the stability (and instability) of periodic solutions near a collision of pure imaginary eigenvalues of opposite signature (the 1: -1 resonance) are obtained
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