Multiplicité des trajectoires fermées de systèmes hamiltoniens connexes

I. Ekeland; L. Lassoued

Annales de l'I.H.P. Analyse non linéaire (1987)

  • Volume: 4, Issue: 4, page 307-335
  • ISSN: 0294-1449

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Ekeland, I., and Lassoued, L.. "Multiplicité des trajectoires fermées de systèmes hamiltoniens connexes." Annales de l'I.H.P. Analyse non linéaire 4.4 (1987): 307-335. <http://eudml.org/doc/78134>.

@article{Ekeland1987,
author = {Ekeland, I., Lassoued, L.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {closed trajectories; strictly positive Gaussian curvature},
language = {fre},
number = {4},
pages = {307-335},
publisher = {Gauthier-Villars},
title = {Multiplicité des trajectoires fermées de systèmes hamiltoniens connexes},
url = {http://eudml.org/doc/78134},
volume = {4},
year = {1987},
}

TY - JOUR
AU - Ekeland, I.
AU - Lassoued, L.
TI - Multiplicité des trajectoires fermées de systèmes hamiltoniens connexes
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1987
PB - Gauthier-Villars
VL - 4
IS - 4
SP - 307
EP - 335
LA - fre
KW - closed trajectories; strictly positive Gaussian curvature
UR - http://eudml.org/doc/78134
ER -

References

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  2. [2] A. Weinstein, Periodic orbits for convex Hamiltonian systems, Ann. of Math., vol. 108, 1078, p. 507-518. Zbl0403.58001MR512430
  3. [3] F. Clarke, Periodic solutions to Hamiltonian inclusions, J. Diff. Equ., vol. 40, 1981, p. 1-6. Zbl0461.34030MR614215
  4. [4] P.H. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure. Appl. Math., vol. 31, 1978, p. 36-68. Zbl0358.70014MR467823
  5. [5] I. Ekeland, Une théorie de Morse pour les systèmes hamiltoniens convexes, Annales I.H.P., Analyse non linéaire, vol. 1, 1984, p. 19-78. Zbl0537.58018MR738494
  6. [6] A. Weinstein, Normal modes for non linear Hamiltonian systems, Inv. Math., vol. 20, 1973, p. 47-57. Zbl0264.70020MR328222
  7. [7] I. Ekeland et J.M. Lasry, On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface, Ann. Math., vol. 12, 1980, p. 283-319. Zbl0449.70014MR592293
  8. [8] H. Berestycki, J.M. Lasry, B. Ruf et G. Mancini, Existence of multiple periodic orbits on star-shaped Hamiltonians surfaces, Comm. Pure. Appl. Math., vol. 38, 1985, p. 252-290. Zbl0569.58027MR784474
  9. [9] I. Ekeland, An index theory for periodic solutions of convex Hamiltonian systems, Nonlinear functional analysis and its applications, F. Browder ed., Proceedings of Symposia in Pure Math., 45, 1986, p. 395-423. Zbl0596.34023MR843575
  10. [10] V. Yakubovich et V. Starzhinsky, Linear Differential Equations with Periodic Coefficients, Halsdedt Press, Wiley, 1980. 
  11. [11] C. Viterbo, Indice des points critiques obtenus par minimaux (à paraître). Zbl0695.58007
  12. [12] I. Ekeland et L. Lassoued, Un flot hamiltonien a au moins deux trajectoires fermées sur toute surface d'énergie convexe et bornée, C.R. Acad. Sc., t. 301, série I, 1985, p. 162-164 Zbl0588.58013MR801952
  13. [13] P.H. Rabinowitz, Periodic solutions of a Hamiltonian system on a prescribed energy surface, J. Diff. Eq., vol. 33, 1979, p. 336-352. Zbl0424.34043MR543703
  14. [14] Glück-Ziller, Exixtence of periodic motions of conservative systems, Seminar on minimal submanifolds, Princeton University Press, 1983. Zbl0546.58040MR795229
  15. [15] Hayashi, Periodic solutions of classical Hamiltonian systems, TokyoJ. Math., vol. 6, 1983. Zbl0498.58010MR732099
  16. [16] V. Benci, Closed geodesics for the Jacobi metric and periodic solutions of prescribed energy of natural Hamiltonian systems, Ann. Inst. H. Poincaré, Analyse non linéaire, 1, 1984, p. 401-411. Zbl0588.35007MR779876
  17. [17] A. Szulkin, Communication personnelle, décembre 1985. 

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