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

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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

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