Abstract
In this paper we study two degree of freedom Hamiltonian systems and applica-
tions to nonlinear wave equations. Near the origin, we assume that near the linearized
system has purely imaginary eigenvalues: ±iw1 and ±iw2, with 0 < w2/w1 << 1 or
w2/w1 >> 1, which is interpreted as a perturbation of a
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