Rotopulsators of the curved N-body problem

Bertrand, 1873, Théorème relatif au mouvement dʼun point attiré vers un centre fixe, C. R. Acad. Sci., 77, 849 Bolyai, 1913 Cariñena, 2005, Central potentials on spaces of constant curvature: The Kepler problem on the two-dimensional sphere S2 and the hyperbolic plane H2, J. Math. Phys., 46, 052702, 10.1063/1.1893214 Diacu, 2011, On the singularities of the curved N-body problem, Trans. Amer. Math. Soc., 363, 2249, 10.1090/S0002-9947-2010-05251-1 Diacu, 2012, Polygonal homographic orbits of the curved 3-body problem, Trans. Amer. Math. Soc., 364, 2783, 10.1090/S0002-9947-2011-05558-3 Diacu, 2013, Relative equilibria in the 3-dimensional curved n-body problem, Mem. Amer. Math. Soc. Diacu, 2012 Diacu, 2013, On the stability of tetrahedral relative equilibria in the positively curved 4-body problem, Phys. D, 256–257, 21, 10.1016/j.physd.2013.04.007 Diacu, 2011, Homographic solutions of the curved 3-body problem, J. Differential Equations, 250, 340, 10.1016/j.jde.2010.08.011 Diacu, 2012, An intrinsic approach in the curved N-body problem. The negative curvature case, J. Differential Equations, 252, 4529, 10.1016/j.jde.2012.01.002 Diacu, 2012, The N-body problem in spaces of constant curvature. Part I: Relative equilibria, J. Nonlinear Sci., 22, 247, 10.1007/s00332-011-9116-z Diacu, 2012, The N-body problem in spaces of constant curvature. Part II: Singularities, J. Nonlinear Sci., 22, 267, 10.1007/s00332-011-9117-y Killing, 1885, Die Mechanik in den nichteuklidischen Raumformen, J. Reine Angew. Math., 98, 1, 10.1515/crll.1885.98.1 Kozlov, 1992, Keplerʼs problem in constant curvature spaces, Celestial Mech. Dynam. Astronom., 54, 393, 10.1007/BF00049149 Liebmann, 1902, Die Kegelschnitte und die Planetenbewegung im nichteuklidischen Raum, Berichte Königl. Sächsischen Gesell. Wiss., Math. Phys. Klasse, 54, 393 Liebmann, 1903, Über die Zentralbewegung in der nichteuklidische Geometrie, Berichte Königl. Sächsischen Gesell. Wiss., Math. Phys. Klasse, 55, 146 Lobachevsky, 1949, The new foundations of geometry with full theory of parallels, 159 Marsden, 1992 Martínez, 2013, On the stability of the Lagrangian homographic solutions in a curved three-body problem on S2, Discrete Contin. Dyn. Syst. Ser. A, 33, 1157, 10.3934/dcds.2013.33.1157 Montaldi, 2000, Relative equilibria and conserved quantities in symmetric Hamiltonian systems, 239 Pérez-Chavela, 2012, An intrinsic approach in the curved N-body problem. The positive curvature case, Trans. Amer. Math. Soc., 364, 3805, 10.1090/S0002-9947-2012-05563-2 Schering, 1870, Die Schwerkraft im Gaussischen Raume, Nachr. Königl. Gesell. Wiss. Göttingen, 15, 311 Shchepetilov, 2006, Nonintegrability of the two-body problem in constant curvature spaces, J. Phys. A, 39, 5787, 10.1088/0305-4470/39/20/011 Wintner, 1947