Global dynamics under a weak potential on a sphere
  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. 
Roberto Castelli, Francesco Paparella and Alessandro Portaluri
math.DS