TY - JOUR
T1 - Singular dynamics under a weak potential on a sphere
AU - Castelli, Roberto
AU - Paparella, Francesco
AU - Portaluri, Alessandro
PY - 2013/6
Y1 - 2013/6
N2 - 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.
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.
KW - Heteroclinics
KW - McGehee coordinates
KW - Regularization of collisions
KW - Singular dynamics
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U2 - 10.1007/s00030-012-0182-1
DO - 10.1007/s00030-012-0182-1
M3 - Article
AN - SCOPUS:84878400845
SN - 1021-9722
VL - 20
SP - 845
EP - 872
JO - Nonlinear Differential Equations and Applications
JF - Nonlinear Differential Equations and Applications
IS - 3
ER -