Central configurations of the N-body problem via equivariant Morse theory. (English) Zbl 0627.58013
En utilisant la théorie équivariante de Morse on donne l’estimation du nombre minimal de configurations centrales dans le problème de N corps en \(E^ 3\). Pour \(N\geq 4\) on constate l’existence de configurations centrales nonplanes.
Reviewer: K.Sibirskij
MSC:
| 58E05 | Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces |
| 70F10 | \(n\)-body problems |
References:
| [1] | Atiyah, M. F., & R. Bott, The Yang-Mills equations over Riemann surfaces, Phil. Trans. R. Soc. London, A 308 (1982), 523–615. · Zbl 0509.14014 · doi:10.1098/rsta.1983.0017 |
| [2] | Bott, R., Lectures on Morse theory, old and new. Bull. Amer. Math. Soc., 7 (1982). · Zbl 0505.58001 |
| [3] | Conley, C. C., Isolated invariant sets and the Morse index, CBMS Regional Conf. Series in Math., 38 (1978), A.M.S., Providence, RI. · Zbl 0397.34056 |
| [4] | Conley, C., & E. Zehnder, Morse-type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math. (to appear). · Zbl 0559.58019 |
| [5] | Fadell, E., & Lee Neuwirth, Configuration spaces, Math. Scand., 10 (1962), 111–118. · Zbl 0136.44104 |
| [6] | Husemoller, D., Fibre Bundles, Springer-Verlag (1966). · Zbl 0144.44804 |
| [7] | Husseini, S., The Topology of Classical Groups and Related Topics, Gordon and Breach, New York (1969). · Zbl 0199.57901 |
| [8] | Pacella, F., Morse theory for flows in presence of a symmetry group, MRC Tech. Summ. Rep. No. 2717. |
| [9] | Palmore, J. I., Measure of degenerate relative equilibria I, Annals of Math., 104 (1976), 421–429. · doi:10.2307/1970964 |
| [10] | Palmore, J. I., New relative equilibria of the N-body problem, Letters Math., Phys., 1 (1976), 119–123. · Zbl 0343.70006 · doi:10.1007/BF00398373 |
| [11] | Palmore, J. I., Classifying relative equilibria, Bull. Amer. Math. Soc., 81 (1975), 489–491. · Zbl 0328.57012 · doi:10.1090/S0002-9904-1975-13794-3 |
| [12] | Palmore, J. I., Central configurations, CW-complexes and the homology of projective plane, Classical Mechanics and Dynamical Systems (1980). · Zbl 0491.70012 |
| [13] | Palmore, J. I., Central configurations of the restricted problem in E 4, J. Diff. Eq., 40 (1981), 291–302. · Zbl 0438.70013 · doi:10.1016/0022-0396(81)90023-1 |
| [14] | Shub, M., Appendix to Smale’s paper: Diagonals and relative equilibria, manifolds, Amsterdam (1970) (Proc. Nuffic Summer School), Lecture Notes. · Zbl 0219.57026 |
| [15] | C. L. Siegel, & J. K. Moser, Lectures on Celestial Mechanics, Springer-Verlag (1971). · Zbl 0312.70017 |
| [16] | E. Spanier, Algebraic Topology, McGraw-Hill Book Company, New York (1966). · Zbl 0145.43303 |
| [17] | A. Wintner, The Analytical Foundation of Celestial Mechanics, Princeton Math. Series, 5 (1941), Princeton University Press, Princeton, NJ. · Zbl 0026.02302 |
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