Asymptotic stability for perturbed Hamiltonian systems (Q1805342)

Several results about asymptotic stability of a perturbed Hamiltonian system of the form \(x' = {\mathcal T \mathcal H}_x(t,x) + R(t,x)\) are proved. Here \(x : [T,\infty) \to \mathbb{R}^{2N}\) and \(\mathcal T\) is the standard \(2N \times 2N\) symplectic matrix. Some of the author's results generalize results of \textit{P. Pucci} and \textit{J. Serrin} [Acta Math. 170, No. 2, 275-307 (1993; Zbl 0797.34059)].