Asymptotic and periodic motion around collinear equilibria in Chermnykh's problem

In this paper we study the asymptotic motion to the collinear equilibrium points of Chermnykh's problem. More specifically, we give three kinds of non-symmetric doubly-asymptotic solutions emanating from L 1 and L 3 . We also show that these solutions are closely connected to the families of periodic orbits generated around these equilibria.