Existence of nonlinear normal modes of symmetric Hamiltonian systems

The authors analyse the existence of nonlinear normal modes of a (nonlinear) Hamiltonian system, i.e. periodic solutions that approximate periodic solutions of the system linearised around an elliptic (and semisimple) equilibrium point. In particular they consider systems with symmetry, including time-reversible symmetry which involves an antisymplectic operator. The general form for such a system contains free parameters (Taylor series coefficients), and their aim is to calculate how the number of nonlinear normal modes varies with these parameters.