Infinite cup length in free loop spaces with an application to a problem of the N-body type

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1. [AC] A. Ambrosetti and V. Coti-Zelati, Periodic Solutions of Singular dynamical Systems, Periodic Solutions of Hamiltonian Systems and Related Topics, P. H. RABINOWITZ et al. Eds., 209, NATO ASI series, Reidel, 1987, pp. 1-10. Zbl0632.34042MR920605
2. [BR] Abbas Bahri and P.H. Rabinowitz, Periodic Solutions of Hamiltonian Systems of the 3-Body Type, Annals Inst. H. Poincaré Analyse non linéaire, Vol. 8, 1991, pp. 561-649. Zbl0745.34034MR1145561
3. [C] V. Coti-Zelati, Periodic Solutions for N-body Type Problems, Preprint 1989. Zbl0703.70009
4. [F1] E. Fadell, Cohomological Methods in Non-Free G-Spaces, with Applications to General Borsuk-Ulam Theorems and Critical Point Theorems for Invariant Functionals, Nonlinear Functional Analysis and its Applications, Reidel1986, pp. 1-47. Zbl0614.55001MR852568
5. [F2] E. Fadell, Lectures in Cohomological Index Theories of G-Spaces with Applications to Critical Point Theory, Raccoltat Di Università della Calabria, 1987, Cosenza, Italy. 
6. [FH1] E. Fadell and S. Husseini, A Note on the Category of the Free Loop Space, Proc. Am. Math. Soc., Vol. 107, 1989, pp. 527-536. Zbl0676.58019MR984789
7. [FH2] E. Fadell and S. Husseini, Category of Loop Spaces of Open Subsets in Euclidean Space, Nonlinear Analysis, Vol. 17, 1991, pp. 1153-1161. Zbl0756.55008MR1137900
8. [G] W. Gordon, Conservative Dynamical Systems Involving Strong Forces, Trans. Am. Math. Soc., Vol. 204, 1975, pp. 113-135. Zbl0276.58005MR377983
9. [H] D. Henderson, Infinite Dimensional Manifolds Are Open Subsets of Hilbert Space, Topology, Vol. 9, 1970, pp. 25-33. Zbl0167.51904MR250342
10. [K] W. Klingenberg, Lectures on Closed Geodesics, Springer-Verlag, GMW No. 230, 1978. Zbl0397.58018MR478069
11. [P] R.S. Palais, Homotopy Theory of Infinite Dimensional Manifolds, Topology, Vol. 5, 1966, pp. 1-16. Zbl0138.18302MR189028
12. [R1] P.H. Rabinowitz, Periodic Solutions for Some Forced Singular Hamiltonian Systems, Festschrift in honor of Jürgen Moser, Analysis Et Cetera, Academic Press, 1990, pp. 521-544. Zbl0790.70019MR1039360
13. [R2] P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, C.B.M.S. Ser. Math., Vol. 65, 1986, A.M.S., Providence, R.I. Zbl0609.58002MR845785
14. [VS] M. Vigué-Poirier and D. Sullivan, The Homology Theory of the Closed Geodesic Problem, J. Diff. Geometry, II, 1976, pp. 633-644. Zbl0361.53058MR455028

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