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We describe a general method, based on a Lyapunov–Schmidt reduction and perturbative techniques, recently used by the authors to find periodic and quasi-periodic solutions both in finite and in infinite dimensional hamiltonian systems. We also illustrate some concrete applications to celestial mechanics and nonlinear wave equation.
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Luca Biasco, Enrico Valdinoci, (Quasi)periodic solutions in (in)finite dimensional Hamiltonian systems with applications to celestial mechanics and wave equation. Port. Math. 65 (2008), no. 4, pp. 431–445DOI 10.4171/PM/1820