Global dynamics under a weak potential on a sphere

Abstract

We give a detailed analytical description of the global dynamics of a point mass moving on a sphere under the action of a logarithmic potential. After performing a McGehee-type blow-up in order to cope with the singularity of the potential, we investigate the rest-points of the flow, the invariant (stable and unstable) manifolds and we give a complete dynamical description of the motion.

20 pages, 6 figures

References in corpus (3)

• A map for eccentric orbits in triaxial potentials
• On the dihedral n-body problem
• On the regularization of the collision solutions of the one-center problem with weak forces