Minimization properties of Hill's orbits and applications to some N-body problems
Arioli, Gianni ; Gazzola, Filippo ; Terracini, Susanna
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000), p. 617-650 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 2000-01-01
@article{AIHPC_2000__17_5_617_0,
     author = {Arioli, Gianni and Gazzola, Filippo and Terracini, Susanna},
     title = {Minimization properties of Hill's orbits and applications to some N-body problems},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {17},
     year = {2000},
     pages = {617-650},
     mrnumber = {1791880},
     zbl = {0977.70006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2000__17_5_617_0}
}

Arioli, Gianni; Gazzola, Filippo; Terracini, Susanna. Minimization properties of Hill's orbits and applications to some N-body problems. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) pp. 617-650. http://gdmltest.u-ga.fr/item/AIHPC_2000__17_5_617_0/

[1] Albouy A., Chenciner A., Le problème des n corps et les distances mutuelles, Invent. Math. 131 (1998) 151-184. | MR 1489897 | Zbl 0919.70005

[2] Ambrosetti A., Critical points and nonlinear variational problems, Mémoire de la Société Mathématique de France 49, 1992. | Numdam | MR 1164129 | Zbl 0766.49006

[3] Ambrosetti A., Coti Zelati V., Periodic solutions of singular Lagrangian systems, Progress in Nonlinear Differential Equations and their Applications, Birkhäuser, 1993. | MR 1267225 | Zbl 0785.34032

[4] Bessi U., Coti Zelati V., Symmetries and noncollision closed orbits for planar N-body-type potentials, Nonlin. Anal. TMA 16 (1991) 587-598. | MR 1094320 | Zbl 0715.70016

[5] Chenciner A., Desolneux N., Minima de l'intégrale d'action et équilibres relatifs de n corps, C. R. Acad. Sci. Paris Ser. I Math. 326 (1998) 1209-1212 (Erratum: C. R. Acad. Sci. Paris Ser. I Math. 327 (1998) 193). | MR 1642007 | Zbl 0922.70009

[6] 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

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

[8] Degiovanni M., Giannoni F., Dynamical systems with Newtonian type potentials, Ann. Sc. Norm. Sup. Pisa Cl. Sci. 15 (1988) 467-494. | Numdam | MR 1015804 | Zbl 0692.34050

[9] Degiovanni M., Giannoni F., Marino A., Dynamical systems with Newtonian type potentials, Atti Acc. Lincei Rend. Fis. Mat. 8 (81) (1987) 271-278. | MR 999819 | Zbl 0667.70010

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

[11] Gordon W., A minimizing property of Keplerian orbits, Amer. J. Math. 99 (5) (1977) 961-971. | MR 502484 | Zbl 0378.58006

[12] Meyer K.R., Hall G.R., Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Springer, 1991. | MR 1140006 | Zbl 0743.70006

[ 13] Moser J., Stable and Random Motions in Dynamical Systems, Princeton Univ. Press, 1973. | MR 442980 | Zbl 0271.70009

[ 14] Moser J., Siegel C.M., Lectures on Celestial Mechanics, Springer, 1971. | MR 502448 | Zbl 0312.70017

[15] Sbano L., Collision solutions of the planar Newtonian three-body problem are not minima of the action functional, Nonlin. Diff. Eq. Appl. (1998).

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

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