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Albouy, A., Chenciner, A., Le problème des n corps et les distances mutuelles, Invent. Math. 131 (1998), 151–184. doi 10.1007/s002220050200AlbouyA.ChencinerA.Invent. Math131199815118410.1007/s002220050200Open DOISearch in Google Scholar
Albouy, A. and Fu, Y., Euler configurations and quasi polynomial systems, Regul. Chaotic Dyn. 12 (2007), 39–55. doi 10.1134/S1560354707010042AlbouyA.FuY.Regul. Chaotic Dyn122007395510.1134/S1560354707010042Open DOISearch in Google Scholar
Albouy, A. and Kaloshin, V., Finiteness of central configurations of five bodies in the plane, Ann. of Math. (2) 176 (2012), 535–588. doi 10.4007/annals.2012.176.1.10AlbouyA.KaloshinV.Ann. of Math217620125355881010.4007/annals.2012.176.1.10Open DOISearch in Google Scholar
Albouy, A., Fu, Y. and Sun, S., Symmetry of planar four-body convex central configurations, Proc. R. Soc. Lond. Ser. A 464 (2008), no. 2093, 1355–1365. doi 10.1098/rspa.2007.0320AlbouyA.FuY.SunS.Proc. R. Soc. Lond. SerA 4642008no. 20931355136510.1098/rspa.2007.0320Open DOISearch in Google Scholar
Casasayas, J., Llibre, J. and Nunes, A., Central configurations of the 1 + n–body problem, Celestial Mechanics and Dynamical Astronomy 60 (1994), 273–288. doi 10.1007/BF00693325CasasayasJ.LlibreJ.NunesA.Celestial Mechanics and Dynamical Astronomy60199427328810.1007/BF00693325Open DOISearch in Google Scholar
Cedó, F. and Llibre, J., Symmetric central configurations of the spatial n–body problem, J. of Geometry and Physics 6 (1989) 367–394. doi 10.1016/0393-0440(89)90010-7CedóF.LlibreJ.J. of Geometry and Physics6198936739410.1016/0393-0440(89)90010-7Open DOISearch in Google Scholar
Corbera, M., Delgado, J., and Llibre, J., On the existence of central configurations of p nested n–gons, Qual. Theory Dyn. Syst. 8 (2009), 255–265. doi 10.1007/s12346-010-0004-yCorberaM.DelgadoJ.LlibreJ.Qual. Theory Dyn. Syst8200925526510.1007/s12346-010-0004-yOpen DOISearch in Google Scholar
Corbera, M. and Llibre, J. Central configurations of nested regular polyhedra for the spatial 2n–body problem, J. of Geometry and Physics 58 (2008), 1241–1252. doi 10.1016/j.geomphys.2008.05.003CorberaM.LlibreJ.J. of Geometry and Physics5820081241125210.1016/j.geomphys.2008.05.003Open DOISearch in Google Scholar
Corbera, M. and Llibre, J., Central configurations of three nested regular polyhedra for the spatial 3n–body problem, J. of Geometry and Physics 59 (2009), 321–339. doi 10.1016/j.geomphys.2008.11.012CorberaM.LlibreJ.J. of Geometry and Physics59200932133910.1016/j.geomphys.2008.11.012Open DOISearch in Google Scholar
Corbera, M. and Llibre, J., Central configurations of nested rotated regular tetrahedra, J. of Geometry and Physics 59 (2009), 137–1394. doi 10.1016/j.geomphys.2009.07.004CorberaM.LlibreJ.J. of Geometry and Physics592009137139410.1016/j.geomphys.2009.07.004Open DOISearch in Google Scholar
Corbera, M. and Llibre, J., On the existence of central configurations of p nested regular polyhedra, Celestial Mech. Dynam. Astronom. 106 (2010), 197–207. doi 10.1007/s10569-009-9254-xCorberaM.LlibreJ.Celestial Mech. Dynam. Astronom106201019720710.1007/s10569-009-9254-xOpen DOISearch in Google Scholar
Corbera, M. and Llibre, J., Central configurations of the 4–body problem with masses m1 = m2 > m3 = m4 = m > 0 and m small, Appl. Math. Comput. 246 (2014), 121–147. doi 10.1016/j.amc.2014.07.109CorberaM.LlibreJ.Appl. Math. Comput246201412114710.1016/j.amc.2014.07.109Open DOISearch in Google Scholar
Cors, J.M., Llibre, J. and Ollé, M., Central configurations of the planar coorbital satellite problem, Celestial Mechanics and Dynamical Astronomy 89 (2004), 319–342. doi 10.1023/B:CELE.0000043569.25307.abCorsJ.M.LlibreJ.OlléM.Celestial Mechanics and Dynamical Astronomy89200431934210.1023/B:CELE.0000043569.25307.abOpen DOISearch in Google Scholar
Diacu, F., Pérez-Chavela, E. and Santoprete, M., Central configurations and total collisions for quasihomogeneous n-body problems, Nonlinear Analysis 65 (2006), 1425–1439. doi 10.1016/j.na.2005.10.023DiacuF.Pérez-ChavelaE.SantopreteM.Nonlinear Analysis6520061425143910.1016/j.na.2005.10.023Open DOISearch in Google Scholar
Dziobek, O., Über einen merkwürdigen Fall des Vielkörperproblems, Astro. Nach. 152 (1900), 32–46.DziobekO.Astro. Nach1521900324610.1002/asna.19001520302Search in Google Scholar
L. Euler, De moto rectilineo trium corporum se mutuo attahentium, Novi Comm. Acad. Sci. Imp. Petrop., 11 (1767), 144–151.EulerL.Novi Comm. Acad. Sci. Imp. Petrop.,111767144151Search in Google Scholar
Fernandes, A.C., Llibre, J. and Mello, L.F., Convex central configurations of the 4–body problem with two pairs of equal masses, Archive for Rational Mechanics and Analysis 226 (2017), 303–320. doi 10.1007/s00205-017-1134-zFernandesA.C.LlibreJ.MelloL.F.Archive for Rational Mechanics and Analysis226201730332010.1007/s00205-017-1134-zOpen DOISearch in Google Scholar
Gómez, G., Llibre, J., Martínez, R. and Simó, C., Dynamics and Mission Design Near Libration Points. Vol. I Fundamentals: The case of collinear libration points, World Scientific Monograph Series in Mathematics, Vol. 2, World Scientific, Singapore, 2001.GómezG.LlibreJ.MartínezR.SimóC.World Scientific Monograph Series in MathematicsVol. 2World ScientificSingapore200110.1142/4402Search in Google Scholar
Gómez, G., Llibre, J., Martínez, R. and Simó, C., Dynamics and Mission Design Near Libration Points. Vol. II Fundamentals: The case of triangular libration points, World Scientific Monograph Series in Mathematics, Vol. 3, World Scientific, Singapore, 2001.GómezG.LlibreJ.MartínezR.SimóC.World Scientific Monograph Series in MathematicsVol. 3World ScientificSingapore200110.1142/4392Search in Google Scholar
Hagihara, Y., Celestial Mechanics, vol. 1, MIT Press, Massachusetts, 1970.HagiharaY.vol. 1MIT PressMassachusetts1970Search in Google Scholar
Hall, G.R.; Central configurations in the planar 1 + n body problem, preprint, 1988 (unpublished).HallG.R.preprint1988(unpublished)Search in Google Scholar
Hampton, M. and Moeckel, R., Finiteness of relative equilibria of the four-body problem, Invent. Math. 163 (2006), no.2, 289–312. doi 10.1007/s00222-005-0461-0HamptonM.MoeckelR.Invent. Math1632006no.228931210.1007/s00222-005-0461-0Open DOISearch in Google Scholar
Lagrange, J.L., Essai sur le problème de toris corps, Ouvres, vol. 6, Gauthier-Villars, Paris, 1873.LagrangeJ.L.Essai sur le problème de toris corpsvol. 6Gauthier-VillarsParis1873Search in Google Scholar
Llibre, J., On the number of central configurations in the N-body problem, Celestial Mech. Dynam. Astronom. 50 (1991), 89–96. doi 10.1007/BF0004898810.1007/BF00048988LlibreJ.On the number of central configurations in the N-body problem501991899610.1007/BF00048988Open DOISearch in Google Scholar
Llibre, J. and Mello, L.F., Triple and Quadruple nested central configurations for the planar n–body problem, Physica D 238 (2009) 563–571. doi 10.1016/j.physd.2008.12.01410.1016/j.physd.2008.12.014LlibreJ.MelloL.F.Triple and Quadruple nested central configurations for the planar n–body problem238200956357110.1016/j.physd.2008.12.014Open DOISearch in Google Scholar
Llibre, J., Moeckel, R. and Simó, C., Central configurations, periodic orbits and Hamiltonian systems, Advances Courses in Math., CRM Barcelona, Birhauser, 2015.LlibreJ.MoeckelR.SimóC.Advances Courses in Math., CRM BarcelonaBirhauser201510.1007/978-3-0348-0933-7Search in Google Scholar
Long, Y. and Sun, S., Four–Body Central Configurations with some Equal Masses, Arch. Rational Mech. Anal. 162 (2002), 24–44. doi 10.1007/s002050100183LongY.SunS.Four–Body Central Configurations with some Equal Masses1622002244410.1007/s002050100183Open DOISearch in Google Scholar
LongLey, W.R., Some particular solutions in the problem of n–bodies, Bull. Amer. Math. Soc. 13 (1907), 324–335.10.1090/S0002-9904-1907-01475-1LongLeyW.R.Some particular solutions in the problem of n–bodies131907324335Open DOISearch in Google Scholar
MacMillan, W.D. and Bartky, W., Permanent configurations in the problem of four bodies, Trans. Amer. Math. Soc. 34 (1932), no. 4, 838–875.10.1090/S0002-9947-1932-1501666-7MacMillanW.D.BartkyW.Permanent configurations in the problem of four bodies341932no. 4838875Open DOISearch in Google Scholar
Maxwell, J.C., On the Stability of Motion of Saturn's Rings, Macmillan & Co., London, 1885.MaxwellJ.C.Macmillan & Co.London1885Search in Google Scholar
Moeckel, R., On central configurations, Mathematische Zeitschrift 205 (1990), no. 4, 499–517.10.1007/BF02571259MoeckelR.On central configurations2051990no. 4499517Open DOISearch in Google Scholar
Moeckel, R., Linear stability of relative equilibria with a dominant mass, J. of Dynamics and Differential Equations 6 (1994), 37–51. doi 10.1007/BF0221918710.1007/BF02219187MoeckelR.Linear stability of relative equilibria with a dominant mass61994375110.1007/BF02219187Open DOISearch in Google Scholar
Moulton, F.R., The straight line solutions of n bodies, Ann. of Math. 12 (1910), 1–17.10.2307/2007159MoultonF.R.The straight line solutions of n bodies121910117Open DOISearch in Google Scholar
Palmore, J., Classifying relative equilibria, Bull. Amer. Math. Soc. 79 (1973), 904–907.10.1090/S0002-9904-1973-13254-9PalmoreJ.Classifying relative equilibria791973904907Open DOISearch in Google Scholar
Pérez-Chavela E., and Santoprete, M., Convex four-body central configurations with some equal masses, Arch. Rational Mech. Anal. 185 (2007), 481–494. doi 10.1007/s00205-006-0047-z10.1007/s00205-006-0047-zPérez-ChavelaE.SantopreteM.Convex four-body central configurations with some equal masses185200748149410.1007/s00205-006-0047-zOpen DOISearch in Google Scholar
Pizzetti, P., Casi particolari del problema dei tre corpi, Rendiconti della Reale Accademia dei Lincei s.5 13 (1904), 17–26.PizzettiP.Casi particolari del problema dei tre corpi1319041726Search in Google Scholar
Robutel, P., and Souchay, J., An introduction to the dynamics of trojan asteroids, in Dvorak, Rudolf; Souchay, Jean, Dynamics of Small Solar System Bodies and Exoplanets, Lecture Notes in Physics 790, Springer, 2010, pp. 197.RobutelP.SouchayJ.An introduction to the dynamics of trojan asteroids790Springer2010pp. 19710.1007/978-3-642-04458-8_4Search in Google Scholar
Saari, D.G., On the role and properties of central configurations, Celestial Mech., 21 (1980), 9–20.10.1007/BF01230241SaariD.G.On the role and properties of central configurations211980920Open DOISearch in Google Scholar
Saari, D.G., Collisions, Rings, and Other Newtonian N-Body Problems, CBMS Regional Conference Series in Mathematics, no. 104, Amer. Math. Soc., Providence, RI, 2005.SaariD.G.Collisions, Rings, and Other Newtonian N-Body Problems104Amer. Math. Soc.Providence, RI200510.1090/cbms/104Search in Google Scholar
Saari, D.G. and Hulkower, N.D., On the manifolds of total collapse orbits and of completely parabolic orbits for the n-body problem, J. Differential Equations 41 (1981), 27–43.10.1016/0022-0396(81)90051-6SaariD.G.HulkowerN.D.On the manifolds of total collapse orbits and of completely parabolic orbits for the n-body problem4119812743Open DOISearch in Google Scholar
Salo, H. and Yoder, C.F., The dynamics of coorbital satellite systems, Astron. Astrophys. 205 (1988), 309–327.SaloH.YoderC.F.The dynamics of coorbital satellite systems205198830932710.1007/978-94-009-2917-3_28Search in Google Scholar
Schmidt, D., Central configurations and relative equilibria for the N-body problem, Classical and celestial mechanics (Recife, 1993/1999), Princeton Univ. Press, Princeton, NJ, (2002), 1–33.SchmidtD.Central configurations and relative equilibria for the N-body problemPrinceton Univ. PressPrinceton, NJ200213310.2307/j.ctv17db3nz.5Search in Google Scholar
Simó, C., Relative equilibrium solutions in the four-body problem, Cel. Mechanics 18 (1978), 165–184.10.1007/BF01228714SimóC.Relative equilibrium solutions in the four-body problem181978165184Open DOISearch in Google Scholar
Smale, S., Mathematical problems for the next century, Math. Intelligencer 20 (1998), no. 2, 7–15. doi 10.1007/BF0302529110.1007/BF03025291SmaleS.Mathematical problems for the next century201998no. 271510.1007/BF03025291Open DOISearch in Google Scholar
Smale, S., Topology and mechanics I, Invent. Math. 10 (1970), 305–331.10.1007/BF01418778SmaleS.Topology and mechanics I101970305331Open DOISearch in Google Scholar
Smale, S., Topology and mechanics II. The planar n-body problem, Invent. Math. 11 (1970), 45–64.10.1007/BF01389805SmaleS.Topology and mechanics II. The planar n-body problem1119704564Open DOISearch in Google Scholar
Wintner, A., The analytical foundations of celestial mechanics, Princeton Math. Series 5, Princeton University Press, Princeton, NJ, 1941.WintnerA.The analytical foundations of celestial mechanics5Princeton University PressPrinceton, NJ1941Search in Google Scholar
Xia, Z., Central configurations with many small masses, J. Differential Equations 91 (1991), 168–179. doi 10.1016/0022-0396(91)90137-X10.1016/0022-0396(91)90137-XXiaZ.Central configurations with many small masses91199116817910.1016/0022-0396(91)90137-XOpen DOISearch in Google Scholar
Zhang, S. and Zhou, Q., Periodic solutions for the 2n–body problems, Proc. Amer. Math. Soc. 131 (2002), 2161–2170.ZhangS.ZhouQ.Periodic solutions for the 2n–body problems13120022161217010.1090/S0002-9939-02-06795-3Search in Google Scholar