Abstract
The author derives a formula for the number M(n, d) of complex nonlinear normal modes in the (n+1) degrees of freedom system with Hamiltonian H2+H, where H2 describes a system of (n+1) uncoupled oscillators with the same frequency (the so-called (1:1:1:.:1) resonance) and H is a generic homogeneous perturbation of degree 2d which Poisson commutes with H2.
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