Bifurcation of closed orbits from equilibria of Newtonian systems with Coriolis forces

Abstract

We consider autonomous Newtonian systems with Coriolis forces in two and three dimensions and study the existence of branches of periodic orbits emanating from equilibria. We investigate both degenerate and nondegenerate situations. While Lyapunov’s center theorem applies locally in the nondegen- erate, nonresonant context, equivariant degree theory provides a global answer which is significant also in some degenerate cases. We apply our abstract results to a problem from Celestial Mechanics. More precisely, in the three-dimensional version of the Restricted Triangular Four- Body Problem with possibly different primaries our results show the existence of at least seven branches of periodic orbits emanating from the stationary points.