Periodic orbits in the restricted three-body problem and Arnold's J+J^+-invariant

We apply Arnold's theory of generic smooth plane curves to Stark-Zeeman systems. This is a class of Hamiltonian dynamical systems that describes the dynamics of an electron in an external electric and magnetic field, and includes many systems from celestial mechanics. Based on Arnold's $J^+$-invariant, we introduce invariants of periodic orbits in planar Stark-Zeeman systems and study their behaviour.Comment: 36 Pages, 16 Figure

On the a and g families of symmetric periodic orbits in the photo-gravitational hill problem and their application to asteroids

This paper focuses on the exploration of families of planar symmetric periodic orbits around minor bodies under the effect of solar radiation pressure. For very small asteroids and comets, an extension of the Hill problem with Solar Radiation Pressure (SRP) perturbation is a particularly well-suited dynamical model. The evolution of the a and g families of symmetric periodic orbits has been studied in this model when SRP is increased from the classical problem with no SRP to levels corresponding to current and future planned missions to minor bodies, as well as one extreme case with very large SRP. In addition, the feasibility an applicability of these orbits for the case of asteroids was analysed, and the effect of SRP in their stability is presented