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


Zbl 0186.58001
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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.