Singular dynamics under a weak potential on a sphere

Roberto Castelli, Francesco Paparella, Alessandro Portaluri

Research output: Contribution to journalArticlepeer-review


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. We perform a McGehee-type blow-up in order to cope with the singularity of the potential when the point mass goes through the singularity. In addition we investigate the rest-points of the flow, the invariant (stable and unstable) manifolds and we give a complete dynamical description of the motion.

Original languageEnglish (US)
Pages (from-to)845-872
Number of pages28
JournalNonlinear Differential Equations and Applications
Issue number3
StatePublished - Jun 2013


  • Heteroclinics
  • McGehee coordinates
  • Regularization of collisions
  • Singular dynamics

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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