Bifurcation of homoclinic orbits for Hamiltonian systems (Q1801432)

The author considers a Hamiltonian ordinary differential equation imbedded in a dissipative family of nonautonomous differential equations depending periodically on the time. Otherwise a nonautonomous non- Hamiltonian perturbation of an autonomous Hamiltonian system is studied. It is supposed that the nonperturbed system admits a hyperbolic periodic solution and homoclinic solutions to such a periodic orbit. A necessary and sufficient condition of bifurcation in the perturbated system, is given (existence of doubly-asymptotic solutions). An asymptotic development of the bifurcated solution and two examples are presented. Since a long time this subject has been very popular in the research groups on ``Nonlinear Dynamics'' of the former Soviet Union. The author's references do not know this relatively ancient contribution.