Global dynamics under a weak potential on a sphere

2011/09/06 by Roberto Castelli, Castelli, Roberto, Francesco Paparella +3
Mathematics · #37C80 #70F10 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37C80 #msc:70F10

paper · pdf · doi:10.48550/arxiv.1109.1128

20 pages, 6 figures

arxiv created 2011/09/06 · arxiv updated 2011/09/07

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.

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