Singular dynamics under a weak potential on a sphere

Roberto Castelli, Francesco Paparella, Alessandro Portaluri

Research output: Contribution to journalArticle

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. 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
Volume20
Issue number3
DOIs
StatePublished - Jun 1 2013

Fingerprint

Singularity
Logarithmic Potential
Stable and Unstable Manifolds
Global Dynamics
Invariant Manifolds
Blow-up
Motion

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

Singular dynamics under a weak potential on a sphere. / Castelli, Roberto; Paparella, Francesco; Portaluri, Alessandro.

In: Nonlinear Differential Equations and Applications, Vol. 20, No. 3, 01.06.2013, p. 845-872.

Research output: Contribution to journalArticle

Castelli, Roberto ; Paparella, Francesco ; Portaluri, Alessandro. / Singular dynamics under a weak potential on a sphere. In: Nonlinear Differential Equations and Applications. 2013 ; Vol. 20, No. 3. pp. 845-872.
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