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A fixed point theorem in symplectic geometry. (English) Zbl 0382.53035

##### MSC:
 53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
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##### References:
 [1] Easton, R. & McGehee, R., to appear. [2] Fong, U. &Meyer, K. R., Algebra of integrals.Revista Columbiana de Matematicas, 9 (1975), 75–90, 1975. · Zbl 0312.58006 [3] Marsden, J. &Weinstein, A., Reduction of symplectic manifolds with symmetry.Rep. Mathematical Physics, 5 (1974), 121–130. · Zbl 0327.58005 [4] McGehee, R. &Meyer, K. R., Homoclinic points of area preserving diffeomorphisms.Amer. J. Math., 96 (1974), 409–421. · Zbl 0298.58007 [5] Meyer, K. R., Symmetries and Integrals in Mechanics.Dynamical Systems (ed. M. Peixoto). Academic Press, 259–272, 1973. · Zbl 0293.58009 [6] Nikishin, N., Fixed points of diffeomorphisms on the two sphere that preserve area.Funkcional Anal. i Prelozen, 8 (1974), 84–85. · Zbl 0323.60067 [7] Poincaré, H.,Méthodes nouvelles de la mécanique céleste, vol. 3. Gauthier-Villars, Paris, 1899, Chap. 28. [8] Simon, C. P., A bound for the fixed point index of an area-preserving map with applications to mechanics,Inventiones Math., 26 (1974), 187–200 and 32 (1976), 101. · Zbl 0331.55006 [9] Sternberg, S.,Lectures on Differential Geometry. Prentice-Hall, Englewood Cliffs, N.J., 1964. · Zbl 0129.13102 [10] Weinstein, A., Lagrangian submanifolds and hamiltonian systems.Ann. Math. (2), 98 (1973), 377–410. · Zbl 0271.58008 [11] –,Lectures on symplectic manifolds. Regional Conference Series in Mathematics, vol. 29., American Math. Soc., Providence, R.I., 1977. · Zbl 0406.53031
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