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Multiple closed orbits for singular conservative systems via geodesic theory. (English) Zbl 0850.70210


MSC:

58E10 Variational problems in applications to the theory of geodesics (problems in one independent variable)
70H05 Hamilton’s equations
70K99 Nonlinear dynamics in mechanics
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References:

[1] S.I. Alber , On periodicity problems in the calculus of variations in the large , A.M.S. Translations , 14 ( 1960 ), pp. 107 - 172 . MR 113234 | Zbl 0094.08202 · Zbl 0094.08202
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[3] A. Ambrosetti - U. Bessi , Multiple periodic trajectories in a relativistic gravitational field , preprint S.N.S., 77 ( 1990 ). MR 1205167 | Zbl 0725.34038 · Zbl 0725.34038
[4] V. Benci - F. GIANNONI, Periodic solutions of prescribed energy for a class of hamiltonian systems with singular potentials , J. Differential Equations , 82 ( 1989 ), pp. 60 - 70 . MR 1023301 | Zbl 0689.34034 · Zbl 0689.34034 · doi:10.1016/0022-0396(89)90167-8
[5] V. Coti Zelati - U. Bessi , Symmetries and non-collision closed orbits for planar, N-body type problems , J. Nonlinear. Analysis , to appear. Zbl 0715.70016 · Zbl 0715.70016 · doi:10.1016/0362-546X(91)90030-5
[6] F. Giannoni - M. DEGIOVANNI, Dynamical systems with newtonian type potentials , Ann. Scuola Norm. Sup. Pisa , 15 ( 1988 ), pp. 467 - 494 . Numdam | MR 1015804 | Zbl 0692.34050 · Zbl 0692.34050
[7] W. Klingenberg , Lectures on Closed Geodesic , Grundlehren der Math. Wiss. , 235 . Zbl 0397.58018 · Zbl 0397.58018
[8] L. Tonelli , Sulle orbite periodiche , Rendiconti R. Accad. dei Lincei , 21 - 1 ( 1912 ), pp. 251 - 258 . JFM 43.0825.04 · JFM 43.0825.04
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