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JOURNALS // Symmetry, Integrability and Geometry: Methods and Applications

SIGMA, 2017, Volume 13, 021, 11 pp. (Mi sigma1221)

Central Configurations and Mutual Differences
D. L. Ferrario

References

1. Albouy A., Open problem 1: are Palmore's “ignored estimates” on the number of planar central configurations correct?, Qual. Theory Dyn. Syst., 14 (2015), 403–406, arXiv: 1501.00694  crossref  mathscinet  zmath  scopus
2. Albouy A., Chenciner A., “Le problème des $n$ corps et les distances mutuelles”, Invent. Math., 131 (1998), 151–184  crossref  mathscinet  zmath
3. Albouy A., Kaloshin V., “Finiteness of central configurations of five bodies in the plane”, Ann. of Math., 176 (2012), 535–588  crossref  mathscinet  zmath  scopus
4. Fadell E. R., Husseini S. Y., Geometry and topology of configuration spaces, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2001  crossref  mathscinet  zmath
5. Fayçal N., “On the classification of pyramidal central configurations”, Proc. Amer. Math. Soc., 124 (1996), 249–258  crossref  mathscinet  zmath
6. Ferrario D. L., “Planar central configurations as fixed points”, J. Fixed Point Theory Appl., 2 (2007), 277–291  crossref  mathscinet  zmath  scopus
7. Ferrario D. L., “Fixed point indices of central configurations”, J. Fixed Point Theory Appl., 17 (2015), 239–251, arXiv: 1412.5817  crossref  mathscinet  zmath  scopus
8. Hampton M., Moeckel R., “Finiteness of relative equilibria of the four-body problem”, Invent. Math., 163 (2006), 289–312  crossref  mathscinet  zmath  scopus
9. Iturriaga R., Maderna E., “Generic uniqueness of the minimal Moulton central configuration”, Celestial Mech. Dynam. Astronom., 123 (2015), 351–361, arXiv: 1406.6887  crossref  mathscinet  zmath  scopus
10. Lang S., Fundamentals of differential geometry, Graduate Texts in Mathematics, 191, Springer-Verlag, New York, 1999  crossref  mathscinet  zmath
11. MacMillan W. D., Bartky W., “Permanent configurations in the problem of four bodies”, Trans. Amer. Math. Soc., 34 (1932), 838–875  crossref  mathscinet
12. Moeckel R., “Relative equilibria of the four-body problem”, Ergodic Theory Dynam. Systems, 5 (1985), 417–435  crossref  mathscinet  zmath  scopus
13. Moeckel R., “On central configurations”, Math. Z., 205 (1990), 499–517  crossref  mathscinet  zmath  scopus
14. Moeckel R., “Central configurations”, Central Configurations, Periodic Orbits, and Hamiltonian Systems, Adv. Courses Math. CRM Barcelona, Birkhäuser/Springer, Basel, 2015, 105–167  crossref  mathscinet
15. Moeckel R., Montgomery R., “Symmetric regularization, reduction and blow-up of the planar three-body problem”, Pacific J. Math., 262 (2013), 129–189, arXiv: 1202.0972  crossref  mathscinet  zmath  scopus
16. Ouyang T., Xie Z., Zhang S., “Pyramidal central configurations and perverse solutions”, Electron. J. Differential Equations, 106 (2004), 9 pp.  mathscinet  zmath
17. Xia Z., “Convex central configurations for the $n$-body problem”, J. Differential Equations, 200 (2004), 185–190  crossref  mathscinet  zmath  scopus


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