A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium
Bartsch, Thomas
Annales de l'I.H.P. Analyse non linéaire, Tome 14 (1997), p. 691-718 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1997-01-01
@article{AIHPC_1997__14_6_691_0,
     author = {Bartsch, Thomas},
     title = {A generalization of the Weinstein-Moser theorems on periodic orbits of a hamiltonian system near an equilibrium},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {14},
     year = {1997},
     pages = {691-718},
     mrnumber = {1482899},
     zbl = {0891.58034},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_1997__14_6_691_0}
}

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, Tome 14 (1997) pp. 691-718. http://gdmltest.u-ga.fr/item/AIHPC_1997__14_6_691_0/

[B1] T. Bartsch, The Conley index over a space, Math. Z., 209, 1992, pp. 167-177 | MR 1147812 | Zbl 0725.58037

[B2] T. Bartsch, Topological Methods for Variational Problems with Symmetries, Lecture Notes in Mathematics, Springer, Berlin Heidelberg, 1560, 1993. | MR 1295238 | Zbl 0789.58001

[B3] T. Bartsch, Bifurcation theory for nonlinear indefinite eigenvalue problems. In preparation.

[BL] S. Bromberg and S. Lopez De Medrano, Le lemme de Morse en classe Cr, r ≥ 1, Preprint.

[Ca] A. Cambini, Sul lemme di Morse, Boll. Unione Mat. Ital., 7, 1973, pp. 87-93 | MR 315738 | Zbl 0267.58007

[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. | MR 512165 | Zbl 0407.47039

[Co] C. Conley, Isolated Invariant Sets and the Morse Index, CBMS, Regional Conf. Ser. in Math., 38, Amer. Math. Soc., Providence, R.I., 1978. | MR 511133 | Zbl 0397.34056

[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. | MR 733717 | Zbl 0559.58019

[tD] T. Tom Dieck, Transformations Groups, de Gruyter, Berlin, 1987. | MR 889050 | Zbl 0611.57002

[D] A. Dold, Lectures on Algebraic Topology, Grundlehren der math. Wiss. 200, Springer, Berlin Heidelberg, 1980. | MR 606196 | Zbl 0434.55001

[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. | MR 478189 | Zbl 0403.57001

[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. | MR 967631 | Zbl 0694.58017

[J] N. Jacobson, Basic Algebra I. Freedman, New York, 1985. | MR 780184 | Zbl 0557.16001

[L] A.M. Lyapunov, Problème général de la stabilité du mouvement, Ann. Fac. Sci., Toulouse, 2, 1907, pp. 203-474. | JFM 38.0738.07 | Numdam | MR 21186

[MW] J. Mawhin and M. Willem, Critical Point Theory and Hamiltonian Systems, Springer, New York, 1989. | MR 982267 | Zbl 0676.58017

[Mo] J. Moser, Periodic orbits near an equilibrium and a theorem by A. Weinstein, Comm. Pure Appl. Math., 29, 1976, pp. 727-747. | Zbl 0346.34024

[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. | MR 845785 | Zbl 0609.58002

[Sa] D. Salamon, Connected simple systems and the Conley index of isolated invariant sets, Trans. Amer. Math. Soc., 291, 1985, pp. 1-41. | MR 797044 | Zbl 0573.58020

[Sp] E. Spanier, Algebraic Topology, McGraw-Hill, New York, 1966. | MR 210112 | Zbl 0145.43303

[W1] A. Weinstein, Normal modes for nonlinear Hamiltonian systems, Inv. math., 20, 1973, pp. 47-57. | MR 328222 | Zbl 0264.70020

[W2] A. Weinstein, Bifurcations and Hamilton's principle, Math. Z., 159, 1978, pp. 235- 248. | MR 501163 | Zbl 0366.58003

[Ya] C.T. Yang, On the theorems of Borsuk-Ulam, Kakutani-Yamabe-Yujòbô and Dyson, Ann. Math., 60, 1954, pp. 262-282. | MR 65910 | Zbl 0057.39104

[Yo] J.A. Yorke, Periods of periodic solutions and the Lipschitz constant, Proc. Amer. Math. Soc., 22, 1963, pp. 509-512. | MR 245916 | Zbl 0184.12103