On periodical motions of a non-autonomous two-degree-of-freedom Hamiltonian system under parametric resonance of the fundamental type

The motion is considered of an almost autonomous 2Π-time-periodic Hamiltonian system with two degrees of freedom. It is assumed that the characteristic index 2ω1 is close to integer i.e. parametric resonance of the fundamental type takes place in the system. The problem about existence of 4Π-periodic system motions, their bifurcation and stability in the rather small neighborhood of coordinate region is solved.