Orbites périodiques de systèmes conservatifs

H. Berestycki

Séminaire Équations aux dérivées partielles (Polytechnique) (1981-1982)

  • page 1-17

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Berestycki, H.. "Orbites périodiques de systèmes conservatifs." Séminaire Équations aux dérivées partielles (Polytechnique) (1981-1982): 1-17. <http://eudml.org/doc/111810>.

@article{Berestycki1981-1982,
author = {Berestycki, H.},
journal = {Séminaire Équations aux dérivées partielles (Polytechnique)},
keywords = {existence and number of periodic solutions; conservative systems; trajectories on sphere; algebraic topology; energy surface},
language = {fre},
pages = {1-17},
publisher = {Ecole Polytechnique, Centre de Mathématiques},
title = {Orbites périodiques de systèmes conservatifs},
url = {http://eudml.org/doc/111810},
year = {1981-1982},
}

TY - JOUR
AU - Berestycki, H.
TI - Orbites périodiques de systèmes conservatifs
JO - Séminaire Équations aux dérivées partielles (Polytechnique)
PY - 1981-1982
PB - Ecole Polytechnique, Centre de Mathématiques
SP - 1
EP - 17
LA - fre
KW - existence and number of periodic solutions; conservative systems; trajectories on sphere; algebraic topology; energy surface
UR - http://eudml.org/doc/111810
ER -

References

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  2. [2] Moser J.: Periodic orbits near an equilibrium and a theorem by Alan Weinstein. Comm. Pure Appl. Math.29, (1976), 727-747. Zbl0346.34024MR426052
  3. [3] Weinstein A.: Normal modes for non linear Hamiltonian systems. Inv. Math., 20 (1973), 47-57. Zbl0264.70020MR328222
  4. [4] Ekeland I.: A perturbation theory near convex Hamlitonian systems. A paraître. Zbl0476.34035
  5. [5] Berestycki H. and Lasry J.M.: Existence of multiple periodic orbits for Hamiltonian systems on a starshaped energy surface. En préparation. 
  6. [6] Rabinowitz P.H.: Periodic solutions of Hamiltonian systems. Comm. Pure Appl. Math.31 (1978) 157-184. Zbl0358.70014MR467823
  7. [7] Weinstein A.: Periodic orbits for convex Hamiltonian systems. Annals Math.108, (1978), 507-518. Zbl0403.58001MR512430
  8. [8] Ekeland I. et Lasry J.M.: On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface. Ann. Math.112 (1980), 283-319. Zbl0449.70014MR592293
  9. [9] Rabinowitz P.H.: Periodic solutions of Hamiltonian systems: A survey. MRC Tech. Summ. Report # 2154 et article à paraître. Zbl0521.58028
  10. [10] Rabinowitz P.H.: A variational method for finding periodic solutions of differential equations.Nonlinear evolution equations (M.G. Crandall editor), Academic Press (1978) pp.222-251. Zbl0486.35009MR513821
  11. [11] Benci V. and Rabinowitz P.H.: Critical point theorems for indefinite functionals, Inv. Math.52, (1979), 336-352. Zbl0465.49006MR537061
  12. [12] Clarke F. and Ekeland I.: Hamiltonian trajectories having prescribed minimal period. Comm. Pure Appl. Math.33, (1980), 103-116. Zbl0403.70016MR562546
  13. [13] Clarke F. and Ekeland I.: Nonlinear oscillations and boundary value problems for Hamiltonian systems. Zbl0514.34032
  14. [14] Rabinowitz P.H.: Subharmonic solutions of Hamiltonian systems. Comm. Pure Appl. Math.33, (1980), 609-633. Zbl0425.34024MR586414
  15. [15] Amann H. and Zehnder E.: Non trivial solutions for a class of non resonance problems and applications. Ann. Scuola Norm. Sup. Pisa, IV, VII (1980), 593-603. Zbl0452.47077
  16. [16] Bahri A. and Berestycki H.: Existence d'une infinité de solutions périodiques de certains systèmes hamiltoniens en présence d'un terme de contrainte. Note C. R. Acad. Sc. Paris292, série A (1981), 315-318. Zbl0471.70019MR608843
  17. [17] Bahri A. and Berestycki H.: Forced vibrations of superquadratic Hamiltonian systems. Acta Mathematica, à paraître. Zbl0592.70027
  18. [18] Bahri A. and Berestycki H.: Existence of forced oscillations for some nonlinear differential équations. A paraître. Zbl0588.34028
  19. [19] Brezis H.: periodic solutions of nonlinear vibrating strings and duality principle. A paraître au Bull. A.M.S. et Proc. Symposium on the mathematical heritage of H. Poincaré. Zbl0537.35055
  20. [20] Berestycki H.and Lasry J.M.: A topological method for the existence of periodic orbits to conservative systems. A paraître. Voir également la Note aux C. R. Acad. Sc. " Orbites périodiques de systèmes conservatifs: résolution de problèmes non-linéaires équivariants sous l'action de S1". A paraître (1982). 
  21. [21] Chow S.N., Mallet-Paret J. and Yorke J.: Global Hopf bifurcation from a multiple eigenvalue. Nonlinear Analysis, T.M.A.2 (1978), 753-763. Zbl0407.47039MR512165
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  23. [23] Ize J.: Bifurcation theory for Fredholm operators. Memoirs A.M.S., 7, n°174, (1976) Zbl0338.47032MR425696
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  26. [26] Fadell E.R., Husseini S.Y. and Rabinowitz P.H.: Borsuk-Ulam theorems for arbitrary S1 actions and applications. MRC tech. Sum. Rep. # 2301 (1981) et et article à paraître. Zbl0506.58010

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