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On the existence of bi--pyramidal central configurations of the $n+2$--body problem with an $n$--gon base
1. | Departament de Tecnologies Digitals i de la Informació, Universitat de Vic, C/. Laura, 13, 08500 Vic, Barcelona, Catalonia, Spain |
2. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Catalonia |
References:
[1] |
F. Cedó and J. Llibre, Symmetric central configurations of the spatial $n$-body problem, J. of Geometry and Physics, 6 (1989), 367-394. |
[2] |
N. Faycal, On the classification of pyramidal central configurations, Proc. Amer. Math. Soc., 124 (1996), 249-258.
doi: 10.1090/S0002-9939-96-03135-8. |
[3] |
E. S. G. Leandro, Finiteness and bifurcations of some symmetrical classes of central configurations, Arch. Ration. Mech. Anal., 167 (2003), 147-177.
doi: 10.1007/s00205-002-0241-6. |
[4] |
X. Liu, On double pyramidal central configuration with parallelogram base, Xinan Shifan Daxue Xuebao Ziran Kexue Ban, 26 (2001), 521-525. |
[5] |
X. Liu, Double pyramidal central configurations with a concave quadrilateral base, J. Chongqing Univ., 1 (2002), 67-69. |
[6] |
X. Liu, A class of double pyramidal central configurations of 7-body with concave pentagon base, Xinan ShifanDaxue Xuebao Ziran Kexue Ban, 27 (2002), 494-496. |
[7] |
X. Liu, Existence and uniqueness for a class of double pyramidal central configurations with a concave pentagonal base, J. Chongqing Univ., 2 (2003), 28-30. |
[8] |
X. Liu and X. Chen, Double pyramidal central configurations of 5-bodieswith arbitrary triangle base, Sichuan Daxue Xuebao, 40 (2003), 190-194. |
[9] |
X. Liu, Existence and uniqueness of a class of double pyramidal central configurations in six-body problems, J. Chongqing Univ., 3 (2004), 97-101. |
[10] |
X. Liu, X. Du and T. Feng, Existence and uniqueness for a class of nine-bodies central configurations, J. Chongqing Univ., 5 (2006), 53-56. |
[11] |
L. F. Mello and A. C. Fernandes, New spatial central configurations in the $5$-body problem, An. Acad. Bras. Ciênc., 83 (2011), 763-774.
doi: 10.1590/S0001-37652011005000023. |
[12] |
L. F. Mello and A. C. Fernandes, New classes of spatial central configurations for the $n+3$ body problem, Nonlinear Anal. Real World Appl., 12 (2011), 723-730.
doi: 10.1016/j.nonrwa.2010.07.013. |
[13] |
R. Moeckel and C. Simó, Bifurcation of spatial central configurations from planar ones, SIAM J. Math. Anal., 26 (1995), 978-998.
doi: 10.1137/S0036141093248414. |
[14] |
T. Ouyang, Z. Xie and S. Zhang, Pyramidal central configurations and perverse solutions, Electron. J. Differential Equations, 106 (2004), 1-9. |
[15] |
D. Yang and S. Zhang, Necessary conditions for central configurations of six-body problems, Southeast Asian Bull. Math., 27 (2003), 739-747. |
[16] |
S. Zhang and Q. Zhou, Double pyramidal central configurations, Phys. Lett. A, 281 (2001), 240-248.
doi: 10.1016/S0375-9601(01)00140-2. |
show all references
References:
[1] |
F. Cedó and J. Llibre, Symmetric central configurations of the spatial $n$-body problem, J. of Geometry and Physics, 6 (1989), 367-394. |
[2] |
N. Faycal, On the classification of pyramidal central configurations, Proc. Amer. Math. Soc., 124 (1996), 249-258.
doi: 10.1090/S0002-9939-96-03135-8. |
[3] |
E. S. G. Leandro, Finiteness and bifurcations of some symmetrical classes of central configurations, Arch. Ration. Mech. Anal., 167 (2003), 147-177.
doi: 10.1007/s00205-002-0241-6. |
[4] |
X. Liu, On double pyramidal central configuration with parallelogram base, Xinan Shifan Daxue Xuebao Ziran Kexue Ban, 26 (2001), 521-525. |
[5] |
X. Liu, Double pyramidal central configurations with a concave quadrilateral base, J. Chongqing Univ., 1 (2002), 67-69. |
[6] |
X. Liu, A class of double pyramidal central configurations of 7-body with concave pentagon base, Xinan ShifanDaxue Xuebao Ziran Kexue Ban, 27 (2002), 494-496. |
[7] |
X. Liu, Existence and uniqueness for a class of double pyramidal central configurations with a concave pentagonal base, J. Chongqing Univ., 2 (2003), 28-30. |
[8] |
X. Liu and X. Chen, Double pyramidal central configurations of 5-bodieswith arbitrary triangle base, Sichuan Daxue Xuebao, 40 (2003), 190-194. |
[9] |
X. Liu, Existence and uniqueness of a class of double pyramidal central configurations in six-body problems, J. Chongqing Univ., 3 (2004), 97-101. |
[10] |
X. Liu, X. Du and T. Feng, Existence and uniqueness for a class of nine-bodies central configurations, J. Chongqing Univ., 5 (2006), 53-56. |
[11] |
L. F. Mello and A. C. Fernandes, New spatial central configurations in the $5$-body problem, An. Acad. Bras. Ciênc., 83 (2011), 763-774.
doi: 10.1590/S0001-37652011005000023. |
[12] |
L. F. Mello and A. C. Fernandes, New classes of spatial central configurations for the $n+3$ body problem, Nonlinear Anal. Real World Appl., 12 (2011), 723-730.
doi: 10.1016/j.nonrwa.2010.07.013. |
[13] |
R. Moeckel and C. Simó, Bifurcation of spatial central configurations from planar ones, SIAM J. Math. Anal., 26 (1995), 978-998.
doi: 10.1137/S0036141093248414. |
[14] |
T. Ouyang, Z. Xie and S. Zhang, Pyramidal central configurations and perverse solutions, Electron. J. Differential Equations, 106 (2004), 1-9. |
[15] |
D. Yang and S. Zhang, Necessary conditions for central configurations of six-body problems, Southeast Asian Bull. Math., 27 (2003), 739-747. |
[16] |
S. Zhang and Q. Zhou, Double pyramidal central configurations, Phys. Lett. A, 281 (2001), 240-248.
doi: 10.1016/S0375-9601(01)00140-2. |
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