Une théorie de Morse pour les systèmes hamiltoniens convexes
Annales de l'I.H.P. Analyse non linéaire (1984)
- Volume: 1, Issue: 1, page 19-78
- ISSN: 0294-1449
Access Full Article
topHow to cite
topEkeland, Ivar. "Une théorie de Morse pour les systèmes hamiltoniens convexes." Annales de l'I.H.P. Analyse non linéaire 1.1 (1984): 19-78. <http://eudml.org/doc/78065>.
@article{Ekeland1984,
author = {Ekeland, Ivar},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Morse index; closed trajectories; periodic solutions; transversality},
language = {fre},
number = {1},
pages = {19-78},
publisher = {Gauthier-Villars},
title = {Une théorie de Morse pour les systèmes hamiltoniens convexes},
url = {http://eudml.org/doc/78065},
volume = {1},
year = {1984},
}
TY - JOUR
AU - Ekeland, Ivar
TI - Une théorie de Morse pour les systèmes hamiltoniens convexes
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1984
PB - Gauthier-Villars
VL - 1
IS - 1
SP - 19
EP - 78
LA - fre
KW - Morse index; closed trajectories; periodic solutions; transversality
UR - http://eudml.org/doc/78065
ER -
References
top- [1] R. Abraham et J. Robbin, Transversal mappings and flows. Benjamin. Zbl0171.44404MR240836
- [2] H. Amann et E. Zehnder, Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equationsAnn. Sc. Norm. Sup. Pisa, t. 7, 1980, p. 539-603. Zbl0452.47077MR600524
- [3] V. Arnold, Chapitres supplémentaires de la théorie des équations différentielles ordinaires. Éditions Mir, 1980 (original russe, 1978). Zbl0455.34001MR626685
- [4] V. Arnold, Méthodes mathématiques de la mécanique classique. Éditions Mir, 1974 (original russe, 1972). Zbl0385.70001
- [5] W. Ballmann, G. Thorbergsson et W. Ziller, Closed geodesies on positively curved manifolds. Annals of Math., t. 116, 1982, p. 213-247. Zbl0495.58010MR672836
- [6] H. Berestycki, J.M. Lasry, G. Mancini et B. Ruf, Existence of multiple periodic orbits on starshaped Hamiltonian surfaces. Preprint, 1983. Zbl0542.58029MR691017
- [7] G. Birkhoff, Dynamical systems. AMS Colloquium Publications, 1927 (réédité, 1966). Zbl53.0732.01MR209095JFM53.0732.01
- [8] R. Bott, Non-degenerate critical manifolds. Ann. of Math., 1954, p. 248-261. Zbl0058.09101
- [9] R. Bott, On the iteration of closed geodesics and Sturm intersection theory. Comm. PAM, t. 9, 1956, p. 176-206. Zbl0074.17202MR90730
- [10] R. Bott, Morse theory, old and new. Bull. AMS (New Series), t. 7, 1982, p. 331-358. Zbl0505.58001MR663786
- [11] F. Clarke, Periodic solutions of Hamiltonian inclusions. J. Diff. Eq., t. 40, 1980, p. 1-6. Zbl0461.34030MR614215
- [12] F. Clarke et I. Ekeland, Hamiltonian trajectories having prescribed minimal period. Comm. Pure App. Math., t. 33, 1980, p. 103-116. Zbl0403.70016MR562546
- [13] C. Conley et E. Zehnder, Morse type index theory for flows and periodic solutions for Hamiltonian equations. Comm. Pure App. Math., to appear. Zbl0559.58019MR733717
- [14] C. Croke et A. Weinstein, Closed curves on convex hypersurfaces and periods of nonlinear oscillations. Inv. Math., t. 64, 1981, p. 199-202. Zbl0471.70020MR629469
- [15] J. Duistermaat, On the Morse index in variational calculus. Advances in Math., t. 21, 1976, p. 173-195. Zbl0361.49026MR649277
- [16] I. Ekeland, Periodic solutions of Hamilton's equations and a theorem of P. Rabinowitz. J. Diff. Eq. t. 34, 1979, p. 523-534. Zbl0446.70019MR555325
- [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. Zbl0449.70014MR592293
- [18] I. Ekeland et R. Temam, Analyse convexe et problèmes variationnels. Dunod-Gauthier-Villars. Zbl0281.49001MR463993
- [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). Zbl0079.10905MR73767
- [20] S. Jorna, ed., Topics is nonlinear dynamics. AIP Conference Proceedings, 1978.
- [21] Klingenberg, Lectures on closed geodesics. Springer, 1981. Zbl0397.58018
- [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. Zbl0041.05602MR36379
- [24] W. Meyer, Kritische Mannigfaltigkeiten in Hilbertmannigfaltigkeiten. Math. Ann., t. 170, 1967, p. 45-66. Zbl0142.21604MR225345
- [25] V. Nemytskii et V. Stepanov, Qualitative theory of differential equations. Princeton University Press, 1960. Zbl0089.29502MR121520
- [26] H. Poincaré, Les méthodes nouvelles de la mécanique céleste. Gauthier-Villars, p. 1892- 1899.
- [27] R. Robinson, The C1 closing lemma, preprint. Zbl0403.58020
- [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. Zbl0308.34001
- [30] I. Ekeland, Dualité et stabilité des systèmes hamiltoniens, CRAS Paris, t. 294, 1982, p. 673-676. Zbl0491.70021MR666432
- [31] I. Ekeland, Une théorie de Morse pour les systèmes hamiltoniens, CRAS Paris, t. 296, 1983, p. 117-120. Zbl0566.58014MR691379
Citations in EuDML Documents
top- V. Brousseau, Espaces de Krein et index des systèmes hamiltoniens
- A. Bahri, P. H. Rabinowitz, Periodic solutions of hamiltonian systems of 3-body type
- Andrzej Szulkin, Morse theory and existence of periodic solutions of convex hamiltonian systems
- Mourad Benabas, Étude d'un système différentiel non linéaire régissant un phénomène gyroscopique forcé
- Claude Viterbo, Intersection de sous-variétés lagrangiennes, fonctionnelles d'action et indice des systèmes hamiltoniens
- Chun-Gen Liu, Yiming Long, Hyperbolic characteristics on star-shaped hypersurfaces
- I. Ekeland, L. Lassoued, Multiplicité des trajectoires fermées de systèmes hamiltoniens connexes
- Antonio Ambrosetti, Vittorio Coti Zelati, Solutions with minimal period for hamiltonian systems in a potential well
- Yiming Long, The minimal period problem of classical hamiltonian systems with even potentials
- Helmut Hofer, Lagrangian embeddings and critical point theory
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.