Une théorie de Morse pour les systèmes hamiltoniens convexes
Annales de l'I.H.P. Analyse non linéaire, Volume 1 (1984) no. 1, p. 19-78
@article{AIHPC_1984__1_1_19_0,
     author = {Ekeland, Ivar},
     title = {Une th\'eorie de Morse pour les syst\`emes hamiltoniens convexes},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {1},
     number = {1},
     year = {1984},
     pages = {19-78},
     zbl = {0537.58018},
     mrnumber = {738494},
     language = {fr},
     url = {http://www.numdam.org/item/AIHPC_1984__1_1_19_0}
}
Ekeland, Ivar. Une théorie de Morse pour les systèmes hamiltoniens convexes. Annales de l'I.H.P. Analyse non linéaire, Volume 1 (1984) no. 1, pp. 19-78. http://www.numdam.org/item/AIHPC_1984__1_1_19_0/

[1] R. Abraham et J. Robbin, Transversal mappings and flows. Benjamin. | MR 240836 | Zbl 0171.44404

[2] H. Amann et E. Zehnder, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations Ann. Sc. Norm. Sup. Pisa, t. 7, 1980, p. 539-603. | Numdam | MR 600524 | Zbl 0452.47077

[3] V. Arnold, Chapitres supplémentaires de la théorie des équations différentielles ordinaires. Éditions Mir, 1980 (original russe, 1978). | MR 626685 | Zbl 0455.34001

[4] V. Arnold, Méthodes mathématiques de la mécanique classique. Éditions Mir, 1974 (original russe, 1972). | Zbl 0385.70001

[5] W. Ballmann, G. Thorbergsson et W. Ziller, Closed geodesies on positively curved manifolds. Annals of Math., t. 116, 1982, p. 213-247. | MR 672836 | Zbl 0495.58010

[6] H. Berestycki, J.M. Lasry, G. Mancini et B. Ruf, Existence of multiple periodic orbits on starshaped Hamiltonian surfaces. Preprint, 1983. | MR 691017

[7] G. Birkhoff, Dynamical systems. AMS Colloquium Publications, 1927 (réédité, 1966). | JFM 53.0732.01 | MR 209095

[8] R. Bott, Non-degenerate critical manifolds. Ann. of Math., 1954, p. 248-261. | Zbl 0058.09101

[9] R. Bott, On the iteration of closed geodesics and Sturm intersection theory. Comm. PAM, t. 9, 1956, p. 176-206. | MR 90730 | Zbl 0074.17202

[10] R. Bott, Morse theory, old and new. Bull. AMS (New Series), t. 7, 1982, p. 331-358. | MR 663786 | Zbl 0505.58001

[11] F. Clarke, Periodic solutions of Hamiltonian inclusions. J. Diff. Eq., t. 40, 1980, p. 1-6. | MR 614215 | Zbl 0461.34030

[12] F. Clarke et I. Ekeland, Hamiltonian trajectories having prescribed minimal period. Comm. Pure App. Math., t. 33, 1980, p. 103-116. | MR 562546 | Zbl 0403.70016

[13] C. Conley et E. Zehnder, Morse type index theory for flows and periodic solutions for Hamiltonian equations. Comm. Pure App. Math., to appear. | MR 733717 | Zbl 0559.58019

[14] C. Croke et A. Weinstein, Closed curves on convex hypersurfaces and periods of nonlinear oscillations. Inv. Math., t. 64, 1981, p. 199-202. | MR 629469 | Zbl 0471.70020

[15] J. Duistermaat, On the Morse index in variational calculus. Advances in Math., t. 21, 1976, p. 173-195. | MR 649277 | Zbl 0361.49026

[16] I. Ekeland, Periodic solutions of Hamilton's equations and a theorem of P. Rabinowitz. J. Diff. Eq. t. 34, 1979, p. 523-534. | MR 555325 | Zbl 0446.70019

[17] I. Ekeland et J.M. Lasry, On the number of closed trajectories for a Hamiltonian flow on a convex energy surface. Ann. Math., t. 112, 1980, p. 283-319. | MR 592293 | Zbl 0449.70014

[18] I. Ekeland et R. Temam, Analyse convexe et problèmes variationnels. Dunod-Gauthier-Villars. | MR 463993 | Zbl 0281.49001

[19] I. Gelfand et V. Lidsky, On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients. Uspekhi Math. Naouk, t. 10, 1955, p. 3-40 (AMS Translation, t. 8, 1958, p. 143-181). | MR 73767 | Zbl 0079.10905

[20] S. Jorna, ed., Topics is nonlinear dynamics. AIP Conference Proceedings, 1978.

[21] Klingenberg, Lectures on closed geodesics. Springer, 1981. | Zbl 0397.58018

[22] M. Krasnosellskii, Topological methods in the theory of nonlinear integral equations. Pergamon Press.

[23] M. Krein, Generalisation of certain investigations of A.M. Liapounov on linear differential equations with periodic coefficients. Doklady Akad. Naouk, USSR, t. 73, 1950, p. 445-448. | MR 36379 | Zbl 0041.05602

[24] W. Meyer, Kritische Mannigfaltigkeiten in Hilbertmannigfaltigkeiten. Math. Ann., t. 170, 1967, p. 45-66. | MR 225345 | Zbl 0142.21604

[25] V. Nemytskii et V. Stepanov, Qualitative theory of differential equations. Princeton University Press, 1960. | MR 121520 | Zbl 0089.29502

[26] H. Poincaré, Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars, p. 1892- 1899.

[27] R. Robinson, The C1 closing lemma, preprint.

[28] M. Struwe, On a critical point theory for minimal surfaces spanning a wire. Bonn preprint SFB n° 569.

[29] V. Yakubovich et V. Starzhinskii, Linear differential equations with periodic coefficients. Halsted Press, John Wiley et Sons. | Zbl 0308.34001

[30] I. Ekeland, Dualité et stabilité des systèmes hamiltoniens, CRAS Paris, t. 294, 1982, p. 673-676. | MR 666432 | Zbl 0491.70021

[31] I. Ekeland, Une théorie de Morse pour les systèmes hamiltoniens, CRAS Paris, t. 296, 1983, p. 117-120. | MR 691379 | Zbl 0566.58014