A continuation principle for periodic solutions of forced motion equations on manifolds and applications to bifurcation theory

We give a continuation principle for forced oscillations of-second order differential equations on not necessarily compact differentiable manifolds. A topological sufficient condition for an equilibrium point to be a bifurcation point for periodic orbits is a straightforward consequence of such a continuation principle. Known results on open sets of euclidean spaces as well as a recent continuation principle for forced oscillations on compact manifolds with nonzero Euler-Poincare characteristic are also included as particular cases.