Invariant tori for semilinear reversible systems Original Research Article

In this paper we consider the problem of the boundedness of all solutions for the oscillator View the MathML source where ω>0 and ω∉N, g(x) is bounded and p(t)=p(t+2π). Since the system in general is non-Hamiltonian, we have to introduce reversibility assumptions to apply the twist theorem for reversible maps. Under some suitable conditions we then obtain the existence of invariant tori and thus the boundedness of all solutions.