A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium

Thomas Bartsch

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 6, page 691-718
  • ISSN: 0294-1449

How to cite


Bartsch, Thomas. "A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium." Annales de l'I.H.P. Analyse non linéaire 14.6 (1997): 691-718. <http://eudml.org/doc/78425>.

author = {Bartsch, Thomas},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Hamiltonian systems; periodic orbits; Weinstein-Moser theorems},
language = {eng},
number = {6},
pages = {691-718},
publisher = {Gauthier-Villars},
title = {A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium},
url = {http://eudml.org/doc/78425},
volume = {14},
year = {1997},

AU - Bartsch, Thomas
TI - A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 6
SP - 691
EP - 718
LA - eng
KW - Hamiltonian systems; periodic orbits; Weinstein-Moser theorems
UR - http://eudml.org/doc/78425
ER -


  1. [B1] T. Bartsch, The Conley index over a space, Math. Z., 209, 1992, pp. 167-177 Zbl0725.58037MR1147812
  2. [B2] T. Bartsch, Topological Methods for Variational Problems with Symmetries, Lecture Notes in Mathematics, Springer, BerlinHeidelberg, 1560, 1993. Zbl0789.58001MR1295238
  3. [B3] T. Bartsch, Bifurcation theory for nonlinear indefinite eigenvalue problems. In preparation. 
  4. [BL] S. Bromberg and S. Lopez De Medrano, Le lemme de Morse en classe Cr, r ≥ 1, Preprint. 
  5. [Ca] A. Cambini, Sul lemme di Morse, Boll. Unione Mat. Ital., 7, 1973, pp. 87-93 Zbl0267.58007MR315738
  6. [CMY] S.N. Chow, J. Mallet-Paret and J.A. Yorke, Global Hopf bifurcation from a multiple eigenvalue. Nonlinear Analysis, T.M.A., 2, 1978, pp. 753-763. Zbl0407.47039MR512165
  7. [Co] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS, Regional Conf. Ser. in Math., 38, Amer. Math. Soc., Providence, R.I., 1978. Zbl0397.34056MR511133
  8. [CoZ] C. Conley and E. Zehnder, Morse type index theory for flows and periodic solutions for Hamiltonian systems, Comm. Pure Appl. Math., 37, 1984, pp. 207-253. Zbl0559.58019MR733717
  9. [tD] T. Tom Dieck, Transformations Groups, de Gruyter, Berlin, 1987. Zbl0611.57002MR889050
  10. [D] A. Dold, Lectures on Algebraic Topology, Grundlehren der math. Wiss.200, Springer, BerlinHeidelberg, 1980. Zbl0434.55001MR606196
  11. [FR] E. Fadell and P.H. Rabinowitz, Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Inv. Math., 45, 1978, pp. 139-174. Zbl0403.57001MR478189
  12. [FZ] A. Floer and E. Zehnder, The equivariant Conley index and bifurcations of periodic solutions of Hamiltonian systems, Ergod. Th. and Dynam. Syst., 8, 1988, pp. 87-97. Zbl0694.58017MR967631
  13. [J] N. Jacobson, Basic Algebra I. Freedman, New York, 1985. Zbl0557.16001MR780184
  14. [L] A.M. Lyapunov, Problème général de la stabilité du mouvement, Ann. Fac. Sci., Toulouse, 2, 1907, pp. 203-474. MR21186JFM38.0738.07
  15. [MW] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989. Zbl0676.58017MR982267
  16. [Mo] J. Moser, Periodic orbits near an equilibrium and a theorem by A. Weinstein, Comm. Pure Appl. Math., 29, 1976, pp. 727-747. Zbl0346.34024
  17. [R] P.H. Rabinovitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, CBMS, Regional Conf. Ser. in Math., 65, Amer. Math. Soc., providence, R.I., 1986. Zbl0609.58002MR845785
  18. [Sa] D. Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. Amer. Math. Soc., 291, 1985, pp. 1-41. Zbl0573.58020MR797044
  19. [Sp] E. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. Zbl0145.43303MR210112
  20. [W1] A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Inv. math., 20, 1973, pp. 47-57. Zbl0264.70020MR328222
  21. [W2] A. Weinstein, Bifurcations and Hamilton's principle, Math. Z., 159, 1978, pp. 235- 248. Zbl0366.58003MR501163
  22. [Ya] C.T. Yang, On the theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujòbô and Dyson, Ann. Math., 60, 1954, pp. 262-282. Zbl0057.39104MR65910
  23. [Yo] J.A. Yorke, Periods of periodic solutions and the Lipschitz constant, Proc. Amer. Math. Soc., 22, 1963, pp. 509-512. Zbl0184.12103MR245916

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.