Periodic solutions of nearly lyapunov system in the external resonance case

The paper deals with the problem of bifurcation of 2π-periodic solutions of a nearly Lyapunov system in the case of external resonance. It gives the method which allows one to construct both the bifurcation curve and the corresponding 2π-periodic solutions in the form of convergent series in fractional powers of a small parameter. As an example, the bifurcation problem of 2π-periodic pendulum motions emerging from its conic motion is considered.