Global Bifurcations of Periodic solutions of the Hill Lunar Problem

Abstract

We describe global bifurcations of non-stationary periodic solutions of the Hill Lunar Problem. Especially we are interested in description of closed connected sets (continua) of non-stationary periodic solutions which bifurcate from stationary ones. Such continua of solutions of the Hill Lunar Problem are not admissible in H12π \ Λ(H). For the Regularized Hill Lunar Problem we prove that these families are unbounded in H12π. As the main tool we use degree theory for SO(2)-equivariant orthogonal maps defined by S.M. Rybicki.