Geodesic
Dynamics and Regularization of the Kepler Problem on Surfaces of Constant Curvature
Canadian journal of mathematics, Tome 69 (2017) no. 5, pp. 961-991

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DOI

We classify and analyze the orbits of the Kepler problem on surfaces of constant curvature (both positive and negative, ${{\mathbb{S}}^{2}}$ and ${{\mathbb{H}}^{2}}$ , respectively) as functions of the angular momentum and the energy. Hill's regions are characterized, and the problem of time-collision is studied. We also regularize the problem in Cartesian and intrinsic coordinates, depending on the constant angular momentum, and we describe the orbits of the regularized vector field. The phase portraits both for ${{\mathbb{S}}^{2}}$ and ${{\mathbb{H}}^{2}}$ are pointed out.
DOI : 10.4153/CJM-2016-014-5
Mots-clés : 70F16, 70G60, Kepler problem on surfaces of constant curvature, Hill's region, singularities, regularization, qualitative analysis of ODE 
Andrade, Jaime; Dàvila, Nestor; Pérez-Chavela, Ernesto; Vidal, Claudio. Dynamics and Regularization of the Kepler Problem on Surfaces of Constant Curvature. Canadian journal of mathematics, Tome 69 (2017) no. 5, pp. 961-991. doi: 10.4153/CJM-2016-014-5
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     author = {Andrade, Jaime and D\`avila, Nestor and P\'erez-Chavela, Ernesto and Vidal, Claudio},
     title = {Dynamics and {Regularization} of the {Kepler} {Problem} on {Surfaces} of {Constant} {Curvature}},
     journal = {Canadian journal of mathematics},
     pages = {961--991},
     year = {2017},
     volume = {69},
     number = {5},
     doi = {10.4153/CJM-2016-014-5},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2016-014-5/}
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