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The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold. (English) Zbl 0516.58017


MSC:

37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
37G99 Local and nonlocal bifurcation theory for dynamical systems

Citations:

Zbl 0386.70001
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References:

[1] Amann, H., Zehnder, E.: Nontrivial solutions for a class of nonresonance problems and applications to nonlinear differential equations. Annali Sc. Norm. Sup. Pisa, Serie IV. Vol.7, 539-603 (1980) · Zbl 0452.47077
[2] Arnold, V.I.: Mathematical methods of classical mechanics. (Appendix 9). Berlin-Heidelberg-New York: Springer 1978
[3] Arnold, V.I.: Proceedings of symposia in pure mathematics. Vol. XXVIII A.M.S., p. 66, 1976
[4] Banyaga, A.: Sur la structure du groupe des difféomorphismes qui préservent une forme symplectique. Comment. Math. Helvetici53, 174-227 (1978) · Zbl 0393.58007 · doi:10.1007/BF02566074
[5] Banyaga, A.: On fixed points of symplectic maps. Preprint · Zbl 0792.58015
[6] Conley, C.C.: Isolated invariant sets and the Morse index. CBMS, Regional Conf. Series in Math., vol. 38 (1978) · Zbl 0397.34056
[7] Conley, C.C., Zehnder, E.: Morse type index theory for flows and periodic solutions for Hamiltonian equations. To appear in Comm. Pure and Appl. Math. · Zbl 0559.58019
[8] Moser, J.: A fixed point theorem in symplectic geometry. Acta Math.141, 17-34 (1978) · Zbl 0382.53035 · doi:10.1007/BF02545741
[9] Moser, J.: Proof of a generalized form of a fixed point theorem due to G.D. Birkooff. Lecture Notes in Mathematics, Vol. 597: Geometry and Topology, pp. 464-494. Berlin-Heidelberg-New York: Springer 1977
[10] Moser, J.: On the volume elements on a manifold. Transactions Amer. Math. Soc.120, 286-294 (1965) · Zbl 0141.19407 · doi:10.1090/S0002-9947-1965-0182927-5
[11] Poincaré, H.: Méthodes nouvelles de la mécanique célèste. Vol. 3, chap. 28. Paris: Gauthier Villars 1899
[12] Weinstein, A.: Lectures on symplectic manifolds. CBMS, Regional conf. series in Math., vol. 29 (1977) · Zbl 0406.53031
[13] Earle, C.J., Eells, J.: A fibre bundle description of Teichmüller theory. J. Diff. Geometry3, 19-43 (1969) · Zbl 0185.32901
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