The theorem of the three closed geodesics
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- by Wilhelm Klingenberg PDF
- Bull. Amer. Math. Soc. 71 (1965), 601-605
References
- S. I. Al′ber, On periodicity problems in the calculus of variations in the large. , Amer. Math. Soc. Transl. (2) 14 (1957), 107–172. MR 0113234, DOI 10.1090/trans2/014/05
- A. I. Fet, Variational problems on closed manifolds, Mat. Sbornik N.S. 30(72) (1952), 271–316 (Russian). MR 0047934
- Wilhelm Klingenberg, On the number of closed geodesics on a riemannian manifold, Bull. Amer. Math. Soc. 70 (1964), 279–282. MR 164307, DOI 10.1090/S0002-9904-1964-11120-4 4. L. Lusternik et L. Schnirelmann, Existence de trois lignes géodésiques fermées sur la surface de genre 0, C. R. Acad. Sci. Paris 188 (1929), 269-271.
- L. Lusternik, Topology of functional spaces and calculus of variations in the large, Trav. Inst. Math. Stekloff 19 (1947), 100 (Russian, with English summary). MR 0025083
- Marston Morse, The calculus of variations in the large, American Mathematical Society Colloquium Publications, vol. 18, American Mathematical Society, Providence, RI, 1996. Reprint of the 1932 original. MR 1451874, DOI 10.1090/coll/018
- Richard S. Palais, Morse theory on Hilbert manifolds, Topology 2 (1963), 299–340. MR 158410, DOI 10.1016/0040-9383(63)90013-2
- R. S. Palais and S. Smale, A generalized Morse theory, Bull. Amer. Math. Soc. 70 (1964), 165–172. MR 158411, DOI 10.1090/S0002-9904-1964-11062-4
- S. Smale, Morse theory and a non-linear generalization of the Dirichlet problem, Ann. of Math. (2) 80 (1964), 382–396. MR 165539, DOI 10.2307/1970398
Additional Information
- Journal: Bull. Amer. Math. Soc. 71 (1965), 601-605
- DOI: https://doi.org/10.1090/S0002-9904-1965-11353-2
- MathSciNet review: 0177374