Morse index properties of colliding solutions to the N-body problem
Annales de l'I.H.P. Analyse non linéaire, Volume 25 (2008) no. 3, p. 539-565
@article{AIHPC_2008__25_3_539_0,
     author = {Barutello, Vivina and Secchi, Simone},
     title = {Morse index properties of colliding solutions to the $N$-body problem},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {25},
     number = {3},
     year = {2008},
     pages = {539-565},
     doi = {10.1016/j.anihpc.2007.02.005},
     zbl = {1143.70006},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2008__25_3_539_0}
}
Barutello, Vivina; Secchi, Simone. Morse index properties of colliding solutions to the $N$-body problem. Annales de l'I.H.P. Analyse non linéaire, Volume 25 (2008) no. 3, pp. 539-565. doi : 10.1016/j.anihpc.2007.02.005. http://www.numdam.org/item/AIHPC_2008__25_3_539_0/

[1] Amann H., Ordinary Differential Equations. An Introduction to Nonlinear Analysis, De Gruyter Studies in Mathematics, vol. 13, W. de Gruyter, 1990. | MR 1071170 | Zbl 0708.34002

[2] Ambrosetti A., Coti Zelati V., Periodic Solutions of Singular Lagrangian Systems, Progr. Nonlinear Differential Equations and their Appl., vol. 10, Birkhäuser Boston Inc., Boston, MA, 1993. | MR 1267225 | Zbl 0785.34032

[3] Bahri A., Rabinowitz P.H., Periodic solutions of Hamiltonian systems of 3-body type, Ann. Inst. H. Poincaré Anal. Non Linéaire 8 (6) (1991) 561-649. | Numdam | MR 1145561 | Zbl 0745.34034

[4] Barutello V., On the n-body problem, Ph.D. thesis, Università di Milano-Bicocca, Milano 2004. Available on-line at, http://www.matapp.unimib.it/.

[5] Barutello V., Ferrario D.L., Terracini S., On the singularities of generalized solutions to the n-body problem, Preprint, 2006. Available on arXiv:, math.DS/0701174.

[6] Chenciner A., Venturelli A., Minima de l’intégrale d’action du problème Newtonien de 4 corps de masses égales dans R 3 : orbites “hip-hop”, Celestial Mech. Dynam. Astronom. 77 (2000) 139-152. | MR 1820355 | Zbl 0984.70009

[7] Coti Zelati V., A class of periodic solutions of the N-body problem, Celestial Mech. Dynam. Astronom. 46 (2) (1989) 177-186. | MR 1044425 | Zbl 0684.70006

[8] Coti Zelati V., Periodic solutions for N-body type problem, Ann. Inst. H. Poincaré Anal. Non Linéaire 7 (5) (1990) 477-492. | Numdam | MR 1138534 | Zbl 0723.70010

[9] Coti Zelati V., Serra E., Collision and non-collision solutions for a class of Keplerian-like dynamical systems, Ann. Mat. Pura Appl. (4) 166 (1994) 343-362. | MR 1313812 | Zbl 0832.70009

[10] Dell'Antonio G., Non-collision periodic solutions of the N-body system, NoDEA, Nonlinear Differential Equations Appl. 5 (1998) 117-136. | MR 1600511 | Zbl 0897.70007

[11] Ferrario D.L., Terracini S., On the existence of collisionless equivariant minimizers for the classical n-body problem, Invent. Math. 155 (2) (2004) 305-362. | MR 2031430 | Zbl 1068.70013

[12] Gordon W., Conservative dynamical systems involving strong forces, Trans. Amer. Math. Soc. 204 (1975) 113-135. | MR 377983 | Zbl 0276.58005

[13] Hampton M., Moeckel R., Finiteness of relative equilibria of the four-body problem, Invent. Math. 163 (2) (2006) 289-312. | MR 2207019 | Zbl 1083.70012

[14] Mcgehee R., Triple collision in the collinear three-body problem, Invent. Math. 27 (1974) 191-227. | MR 359459 | Zbl 0297.70011

[15] Moeckel R., On central configurations, Math. Z. 205 4 (1990) 499-517. | MR 1082871 | Zbl 0684.70005

[16] Pacella F., Central configurations and the equivariant Morse theory, Arch. Ration. Mech. Anal. 97 (1987) 59-74. | MR 856309 | Zbl 0627.58013

[17] Painlevé P., Leçons sur la théorie analytique des équations différentielles, Hermann, Paris, 1897. | JFM 28.0262.01

[18] Pollard H., Celestial Mechanics, Carus Mathematical Monographs, vol. 18, Mathematical Association of America, 1976. | MR 434057 | Zbl 0353.70009

[19] Riahi H., Study of the generalized solutions of n-body type problems with weak force, Nonlinear Anal. 28 (1) (1997) 49-59. | MR 1416033 | Zbl 0914.70007

[20] Serra E., Avoiding collisions in singular potential problems, in: Variational Methods in Nonlinear Analysis, Erice, 1992, Gordon and Breach, Basel, 1995, pp. 173-185. | MR 1451160 | Zbl 0845.34048

[21] Serra E., Terracini S., Collisionless periodic solutions to some three-body problems, Arch. Ration. Mech. Anal. 120 (4) (1992) 305-325. | MR 1185563 | Zbl 0773.70009

[22] Serra E., Terracini S., Noncollision solutions to some singular minimization problems with Keplerian-like potentials, Nonlinear Anal. 22 (1) (1994) 45-62. | MR 1256169 | Zbl 0813.70006

[23] Shub M., Diagonal and Relative Equilibria, Lecture Notes in Math., vol. 197, Springer, Berlin, 1971. | MR 278700

[24] Sperling H.J., On the real singularities of the N-body problem, J. Reine Angew. Math. 245 (1970) 15-40. | MR 290630 | Zbl 0207.23301

[25] Sundman K.F., Mémoire sur le problème des trois corps, Acta Math. 36 (1913) 105-179. | JFM 43.0826.01 | MR 1555085

[26] Tanaka K., Non-collision solutions for a second order singular Hamiltonian system with weak force, Ann. Inst. H. Poincaré 10 (2) (1993) 215-238. | Numdam | MR 1220034 | Zbl 0781.58036

[27] Terracini S., Venturelli A., Symmetric trajectories for the 2N-body problem with equal masses, Arch. Ration Mech. Anal. 184 (2007) 465-493. | MR 2299759 | Zbl 1111.70010

[28] Wintner A., The Analytical Foundation of Celestial Mechanics, Princeton University Press, Princeton, NJ, 1941. | JFM 67.0785.01 | MR 5824 | Zbl 0026.02302

[29] Von Zeipel H., Sur les singularités du problème des n corps, Ark. Math. Astr. Fys. 4 (32) (1908). | JFM 39.0792.14