Persistence of Invariant Tori in Integrable Hamiltonian Systems Under Almost Periodic Perturbations

In this paper, we are concerned with the existence of invariant tori in nearly integrable Hamiltonian systems H = h(y) + f (x, y, t), where y is an element of D subset of R-n with D being an open bounded domain, x is an element of T-n, f (x, y, t) is a real analytic almost periodic function in t with the frequency omega = (. . . , omega(lambda), . . .)(lambda)(is an element of Z) is an element of R-Z. As an application, we will prove the existence of almost periodic solutions and the boundedness of all solutions for the second-order differential equations with superquadratic potentials depending almost periodically on time.