Dynamics and bifurcation near the transition from stability to complex instability: an analytical approach using normal forms
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We consider a Hamiltonian of three degrees of freedom and a family of periodic orbits with a transition from stability to complex instability, such that there is an irrational collision of the Floquet eigenvalues of opposite sign. We analize the local dynamics and the bifurcation phenomena linked to this transition. We study the resulting Hamiltonian Hopf-like bifurcation from an analy- tical point of view by means of normal forms. The existence of a bifurcating family of 2D tori is derived in both cases (direct and inverse bifur- cation) are described.