@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}, pages = {19--78}, publisher = {Gauthier-Villars}, volume = {1}, number = {1}, year = {1984}, mrnumber = {738494}, zbl = {0537.58018}, language = {fr}, url = {http://archive.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, Tome 1 (1984) no. 1, pp. 19-78. http://archive.numdam.org/item/AIHPC_1984__1_1_19_0/
[1] Transversal mappings and flows. Benjamin. | MR | Zbl
et ,[2] 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 | Zbl
et ,[3] Chapitres supplémentaires de la théorie des équations différentielles ordinaires. Éditions Mir, 1980 (original russe, 1978). | MR | Zbl
,[4] Méthodes mathématiques de la mécanique classique. Éditions Mir, 1974 (original russe, 1972). | Zbl
,[5] Closed geodesies on positively curved manifolds. Annals of Math., t. 116, 1982, p. 213-247. | MR | Zbl
, et ,[6] Existence of multiple periodic orbits on starshaped Hamiltonian surfaces. Preprint, 1983. | MR
, , et ,[7] Dynamical systems. AMS Colloquium Publications, 1927 (réédité, 1966). | JFM | MR
,[8] Non-degenerate critical manifolds. Ann. of Math., 1954, p. 248-261. | Zbl
,[9] On the iteration of closed geodesics and Sturm intersection theory. Comm. PAM, t. 9, 1956, p. 176-206. | MR | Zbl
,[10] Morse theory, old and new. Bull. AMS (New Series), t. 7, 1982, p. 331-358. | MR | Zbl
,[11] Periodic solutions of Hamiltonian inclusions. J. Diff. Eq., t. 40, 1980, p. 1-6. | MR | Zbl
,[12] Hamiltonian trajectories having prescribed minimal period. Comm. Pure App. Math., t. 33, 1980, p. 103-116. | MR | Zbl
et ,[13] Morse type index theory for flows and periodic solutions for Hamiltonian equations. Comm. Pure App. Math., to appear. | MR | Zbl
et ,[14] Closed curves on convex hypersurfaces and periods of nonlinear oscillations. Inv. Math., t. 64, 1981, p. 199-202. | MR | Zbl
et ,[15] On the Morse index in variational calculus. Advances in Math., t. 21, 1976, p. 173-195. | MR | Zbl
,[16] Periodic solutions of Hamilton's equations and a theorem of P. Rabinowitz. J. Diff. Eq. t. 34, 1979, p. 523-534. | MR | Zbl
,[17] On the number of closed trajectories for a Hamiltonian flow on a convex energy surface. Ann. Math., t. 112, 1980, p. 283-319. | MR | Zbl
et ,[18] Analyse convexe et problèmes variationnels. Dunod-Gauthier-Villars. | MR | Zbl
et ,[19] 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 | Zbl
et ,[20] Topics is nonlinear dynamics. AIP Conference Proceedings, 1978.
, ed.,[21] Zbl
, Lectures on closed geodesics. Springer, 1981. |[22] Topological methods in the theory of nonlinear integral equations. Pergamon Press.
,[23] 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 | Zbl
,[24] Kritische Mannigfaltigkeiten in Hilbertmannigfaltigkeiten. Math. Ann., t. 170, 1967, p. 45-66. | MR | Zbl
,[25] Qualitative theory of differential equations. Princeton University Press, 1960. | MR | Zbl
et ,[26] Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars, p. 1892- 1899.
,[27] The C1 closing lemma, preprint.
,[28] On a critical point theory for minimal surfaces spanning a wire. Bonn preprint SFB n° 569.
,[29] Linear differential equations with periodic coefficients. Halsted Press, John Wiley et Sons. | Zbl
et ,[30] Dualité et stabilité des systèmes hamiltoniens, CRAS Paris, t. 294, 1982, p. 673-676. | MR | Zbl
,[31] Une théorie de Morse pour les systèmes hamiltoniens, CRAS Paris, t. 296, 1983, p. 117-120. | MR | Zbl
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