Singular dynamics under a weak potential on a sphere

Roberto Castelli; Francesco Paparella; Alessandro Portaluri

doi:10.1007/s00030-012-0182-1

Singular dynamics under a weak potential on a sphere

Roberto Castelli, Francesco Paparella, Alessandro Portaluri

Mathematics

Research output: Contribution to journal › Article › peer-review

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 language	English (US)
Pages (from-to)	845-872
Number of pages	28
Journal	Nonlinear Differential Equations and Applications
Volume	20
Issue number	3
DOIs	https://doi.org/10.1007/s00030-012-0182-1
State	Published - Jun 2013

Keywords

Heteroclinics
McGehee coordinates
Regularization of collisions
Singular dynamics

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1007/s00030-012-0182-1

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AU - Paparella, Francesco

AU - Portaluri, Alessandro

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AB - 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.

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KW - McGehee coordinates

KW - Regularization of collisions

KW - Singular dynamics

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Singular dynamics under a weak potential on a sphere

Abstract

Keywords

ASJC Scopus subject areas

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