Stability and bifurcation phenomena in asymptotically Hamiltonian systems

The influence of time-dependent perturbations on an autonomous Hamiltonian system with equilibrium center type is considered. It assumed that the decay at infinity in time and vanish unperturbed system. In this case stability long-term behaviour trajectories depend nonlinear non-autonomous terms equations. paper investigates bifurcations associated a change Lyapunov emergence new attracting or repelling states perturbed asymptotically dependence structure decaying discussed.