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Reduction of symplectic manifolds with symmetry. (English) Zbl 0327.58005

37J15 Symmetries, invariants, invariant manifolds, momentum maps, reduction (MSC2010)
53D20 Momentum maps; symplectic reduction
57S25 Groups acting on specific manifolds
70H33 Symmetries and conservation laws, reverse symmetries, invariant manifolds and their bifurcations, reduction for problems in Hamiltonian and Lagrangian mechanics
Full Text: DOI
[1] Abraham, R.; Marsden, J., Foundations of mechanics, (1967), Benjamin New York, N.Y
[2] Arnold, V., Ann. inst. Grenoble, 16, 319, (1966)
[3] Bourbaki, N., Variétés différentielles et analytiques, fascicule de résultants, (), Topologie Générale, (1960), Hermann Paris, Livre III, ch. 3, Fasc. III
[4] Carathéodory, C., Calculus of variations and partial differential equations of the first order, (1965), Holden-Day San Francisco, [Translation of German edition, B. G. Teubner, Berlin, 1935] · Zbl 0134.31004
[5] Ebin, D., Proc. symp. pure math. XV, Amer. math. soc., 11, (1970)
[6] Ebin, D.; Marsden, J., Ann. of math., 92, 102, (1970) · Zbl 0211.57401
[7] Fischer, A.; Marsden, J.; Fischer, A.; Marsden, J., Journ. math. phys., Comm. math. phys., 28, 1, (1972)
[8] Fischer, A., and J. Marsden, General relativity as a Hamiltonian system, Symposia Mathematica (to appear). · Zbl 0305.53051
[9] Iacob, A., Rev. roum. math. pures et appl., XVI, 1497, (1971), Tome
[10] Kostant, B., Quantization and unitary representations, (), 87-208
[11] Marsden, J., Arch. rat. mech. an., 28, 362, (1968)
[12] Marsden, J.; Ebin, D.; Fischer, A., Diffeomorphism groups, hydrodynamics and relativity, Proc. can. math. congress, XIII, 135, (1972)
[13] Marsden, J.; Ebin, D.; Fischer, A.; Abraham, R., (), 237
[14] Poincaré, H., LES méthodes nouveles de la méchanique céleste, (1892), Gauthier-Villars Paris
[15] Robbin, J., Relative equilibria in mechanical systems, (to appear). · Zbl 0273.58005
[16] Roels, J.; Weinstein, A., J. math. phys., 12, 1482, (1971)
[17] Segal, I., Journ. de math. pures et app., XLIV, 71, (1965)
[18] Smale, S.; Smale, S., Inv. math., Inv. math., 11, 45, (1970)
[19] Sniatycki, J.; Tulczyjew, W.M., Ann. inst. H. Poincaré, 15, 3, 177, (1971)
[20] Souriau, J.M., Structure des systémes dynamiques, (1970), Dunod Paris · Zbl 0186.58001
[21] Weinstein, A., Adv. in math., 3, 329, (1971)
[22] Whittaker, E.T., Analytical dynamics, (1937), Cambridge Univ. Press Cambridge, England · Zbl 0974.70001
[23] Meyer, K., Symmetries and integrals in mathematics, (), 259-272
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