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),<graphic></graphic>where y∈D⊆Rn<inline-graphic></inline-graphic> with D being an open bounded domain, x∈Tn<inline-graphic></inline-graphic>, f(x, y, t) is a real analytic almost periodic function in t with the frequency ω=(…,ωλ,…)λ∈Z∈RZ<inline-graphic></inline-graphic>. 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. [ABSTRACT FROM AUTHOR]