Homoclinic solutions for eventually autonomous high-dimensional Hamiltonian systems. (Q1856870)

The geometry of stable and unstable manifolds was analyzed to study homoclinic solutions for eventually autonomous planar flows as was already done by \textit{A. Ambrosetti} and \textit{V. Coti Zelati} [Rend. Semin. Mat. Univ. Padova 89, 177--194 (1993; Zbl 0806.58018)], but here the analysis is extended to higher-dimensional systems. The problem is formulated as the existence of intersection points between two Lagrangian manifolds. Critical points correspond to homoclinic solutions. The new feature in high dimension is that twice as many homoclinic solutions are found.