Bulletin (New Series) of the American Mathematical Society
- Bull. Amer. Math. Soc. (N.S.)
- Volume 5, Number 1 (1981), 1-13.
Symplectic geometry
Full-text: Open access
Article information
Source
Bull. Amer. Math. Soc. (N.S.) Volume 5, Number 1 (1981), 1-13.
Dates
First available in Project Euclid: 4 July 2007
Permanent link to this document
http://projecteuclid.org/euclid.bams/1183548217
Mathematical Reviews number (MathSciNet)
MR614310
Zentralblatt MATH identifier
0465.58013
Subjects
Primary: 58F05
Citation
Weinstein, Alan. Symplectic geometry. Bull. Amer. Math. Soc. (N.S.) 5 (1981), no. 1, 1--13. http://projecteuclid.org/euclid.bams/1183548217.
References
- [A-M] R. Abraham and J. Marsden, Foundations of mechanics, 2nd ed., Benjamin/Cummings, Reading, Mass., 1978.
- [AR] V. I. Arnold, Mathematical methods of classical mechanics, Graduate Texts in Math., vol. 60, Springer-Verlag, Berlin and New York, 1978.
- [AU-K] L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), 255-354.Zentralblatt MATH: 0233.22005
Mathematical Reviews (MathSciNet): MR293012
Digital Object Identifier: doi: 10.1007/BF01389744 - [BI] G. D. Birkhoff, Fifty years of American mathematics, Semicentennial Addresses of Amer. Math. Soc., 1938, p. 307.
- [BO] C. E. Bond, Biology of fishes, Sanders, Philadelphia, Pa., 1979.
- [BU] L. Boutet de Monvel, private communication.
- [BU-G] L. Boutet de Monvel and V. Guillemin, The spectral theory of Toeplitz operators, preprint.
- [C] S. S. Chern, From triangles to manifolds, Amer. Math. Monthly 86 (1979), 339-349.Zentralblatt MATH: 0425.53002
Mathematical Reviews (MathSciNet): MR528789
Digital Object Identifier: doi: 10.2307/2321093 - [D] J. J. Duistermaat, Applications of Fourier integral operators, Proc. Internat. Congr. Math. (Vancouver, 1974), Canadian Mathematical Congress, 1975, pp. 263-268.
- [D-H] J. J. Duistermaat and L. Hörmander, Fourier integral operators. II, Acta Math. 128 (1972), 183-269.Zentralblatt MATH: 0232.47055
Mathematical Reviews (MathSciNet): MR388464
Digital Object Identifier: doi: 10.1007/BF02392165 - [F-Z] L. Faddeev and V. Zaharov, Korteweg-de Vries equation: a completely integrable Hamiltonian system, Funkcional. Anal. i Priložen 5 (1971), 18-27.
- [G] V. W. Guillemin, Clean intersection theory and Fourier integral operators, Lecture Notes in Math., vol. 459, Springer-Verlag, Berlin and New York, 1975, pp. 23-35.Zentralblatt MATH: 0315.42012
Mathematical Reviews (MathSciNet): MR415689
Digital Object Identifier: doi: 10.1007/BFb0074191 - [G-S1] V. W. Guillemin and S. Sternberg, Geometric asymptotics, Amer. Math. Soc., Providence, R. I., 1976.Zentralblatt MATH: 0364.53011
- [G-S2] V. W. Guillemin and S. Sternberg, Some problems in integral geometry and some related problems in micro-local analysis, Amer. J. Math. 101 (1979), 915-955.Zentralblatt MATH: 0446.58019
Mathematical Reviews (MathSciNet): MR536046
Digital Object Identifier: doi: 10.2307/2373923 - [H-K] P. de la Harpe and M. Karoubi, Perturbations compactes des representations d'un groupe dans un espace de Hilbert, Bull. Soc. Math. France Mém. 46 (1976), 41-65.Zentralblatt MATH: 0331.46051
- [HR] L. Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), 79-183.Zentralblatt MATH: 0212.46601
Mathematical Reviews (MathSciNet): MR388463
Digital Object Identifier: doi: 10.1007/BF02392052 - [K-K-S] D. Kazhdan, B. Kostant, and S. Sternberg, Hamiltonian group actions and dynamical systems of Calogero Type, Comm. Pure Appl. Math. 31 (1978), 481-508.Zentralblatt MATH: 0368.58008
Mathematical Reviews (MathSciNet): MR478225
Digital Object Identifier: doi: 10.1002/cpa.3160310405 - [KI1] A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk. 17 (1962), 57-110. (English translation in Russian Math. Surveys, 53, 104).
- [KI2] A. A. Kirillov, Elements of the theory of representations, Springer-Verlag, Berlin and New York, 1976.
- [KO1] B. Kostant, Quantization and unitary representations: Part I, Prequantization, Lecture Notes in Math., vol. 170, Springer-Verlag, Berlin and New York, 1970, pp. 87-208.Zentralblatt MATH: 0223.53028
Mathematical Reviews (MathSciNet): MR294568
Digital Object Identifier: doi: 10.1007/BFb0079068 - [KO2] B. Kostant, The solution to a generalized Toda lattice and representation theory, Advances in Math. 34 (1979), 195-338.Zentralblatt MATH: 0433.22008
Mathematical Reviews (MathSciNet): MR550790
Digital Object Identifier: doi: 10.1016/0001-8708(79)90057-4 - [LA1] J. L. Lagrange, Mémoire sur la théorie des variations des éléments des planètes, Mémoires de la classe des sciences mathématiques et physiques de l'institut de France, 1808, pp. 1-72.
- [LA2] J. L. Lagrange, Second mémoire sur la théorie de la variation des constantes arbitraires dans les problèmes de mécanique, Mémoires de la classe des sciences mathématiques et physiques de l'institut de France 1809, pp. 343-352.
- [LI] R. G. Littlejohn, A guiding center Hamiltonian: A new approach, J. Math. Phys. 20 (1979), 2445-2458.Zentralblatt MATH: 0444.70020
Mathematical Reviews (MathSciNet): MR553507
Digital Object Identifier: doi: 10.1063/1.524053 - [M] G.-M. Marle, Symplectic manifolds, dynamical groups, and Hamiltonian mechanics, in Differential Geometry and Relativity (Cahen and Flato (eds.)), D. Reidel, Dordrecht, 1976, pp. 249-269.Zentralblatt MATH: 0369.53042
Mathematical Reviews (MathSciNet): MR438393
Digital Object Identifier: doi: 10.1007/978-94-010-1508-0_22 - [MA-W] J. Marsden and A. Weinstein, Reduction of symplectic manifolds with symmetry, Reports on Math. Phys. 5 (1974), 121-130.Zentralblatt MATH: 0327.58005
Mathematical Reviews (MathSciNet): MR402819
Digital Object Identifier: doi: 10.1016/0034-4877(74)90021-4 - [MAS] V. P. Maslov, Théorie des perturbations et méthodes asymptotiques, Dunod, Gauthier-Villars, Paris, 1972. (Translation of 1965 Russian edition.)Zentralblatt MATH: 0247.47010
- [MEL1] R. B. Melrose, Equivalence of glancing hypersurfaces, Invent. Math. 37 (1976), 165-191.Zentralblatt MATH: 0354.53033
Mathematical Reviews (MathSciNet): MR436225
Digital Object Identifier: doi: 10.1007/BF01390317 - [MEL2] R. B. Melrose, Forward scattering by a convex obstacle, Comm. Pure Appl. Math. 33 (1980), 461-499.Zentralblatt MATH: 0435.35066
Mathematical Reviews (MathSciNet): MR575734
Digital Object Identifier: doi: 10.1002/cpa.3160330402 - [MEY] K. Meyer, Symmetries and integrals in mechanics, in Dynamical Systems (M. Peixoto (ed)), Academic Press, New York, 1973, pp. 259-273.
- [MI-F] A. S. Miščenko and A. T. Fomenko, Euler equations on finite-dimensional Lie groups, Math. USSR-Izv. 12 (1978), 371-389.
- [MO] J. Moser, A fixed point theorem in symplectic geometry, Acta Math. 141 (1978), 17-34.Zentralblatt MATH: 0382.53035
Mathematical Reviews (MathSciNet): MR478228
Digital Object Identifier: doi: 10.1007/BF02545741 - [R-W] L. Rothschild and J. Wolf, Representations of semi-simple groups associated to nilpotent orbits, Ann. Sci. École Norm. Sup. (4) 7 (1974), 155-174.
- [S-K-K] M. Sato, T. Kawai and M. Kashiwara, Microfunctions and partial differential equations, Lecture Notes in Math., vol. 287, Springer-Verlag, Berlin and New York, 1973, pp. 265-529.
- [SE] I. E. Segal, Quantization of nonlinear systems, J. Math. Phys. 1 (1960), 468-488.Zentralblatt MATH: 0099.22402
Mathematical Reviews (MathSciNet): MR135093
Digital Object Identifier: doi: 10.1063/1.1703683 - [SI] B. Simon, The classical limit of quantum partition functions, Comm. Math. Phys. 71 (1980), 247-276.Zentralblatt MATH: 0436.22012
Mathematical Reviews (MathSciNet): MR565281
Digital Object Identifier: doi: 10.1007/BF01197294
Project Euclid: euclid.cmp/1103907536 - [SN] J. Sniatycki, Geometric quantization and quantum mechanics, Springer-Verlag, New York, 1980.
- [SN-T] J. Sniatycki and W. M. Tulczyjew, Generating forms of lagrangian submanifolds, Indiana Univ. Math. J. 22 (1972), 267-275.Zentralblatt MATH: 0237.58002
Mathematical Reviews (MathSciNet): MR305297
Digital Object Identifier: doi: 10.1512/iumj.1972.22.22021 - [SO] J.-M. Souriau, Structure des systemes dynamiques, Dunod, Paris, 1970.
- [ST] S. Sternberg, Celestial mechanics. II, W. A. Benjamin, New York, 1969.Zentralblatt MATH: 0194.56702
- [T] M. E. Taylor, Grazing rays and reflection of singularities of solutions to wave equations, Comm. Pure Appl. Math. 24 (1976), 1-38.Zentralblatt MATH: 0318.35009
Mathematical Reviews (MathSciNet): MR397175
Digital Object Identifier: doi: 10.1002/cpa.3160290102 - [WA] N. R. Wallach, Symplectic geometry and Fourier analysis, Math. Sci. Press, Brookline, Mass., 1977.
- [WE1] A. Weinstein, On Maslov's quantization condition, Lecture Notes in Math., vol. 459, Springer-Verlag, Berlin and New York, 1975, pp. 341-372.Zentralblatt MATH: 0348.58016
Mathematical Reviews (MathSciNet): MR436231
Digital Object Identifier: doi: 10.1007/BFb0074200 - [WE2] A. Weinstein, Fourier integral operators, quantization, and the spectra of riemannian manifolds, Colloques Internationaux du CNRS 237 (1976), 289-298.
- [WE3] A. Weinstein, Lectures on symplectic manifolds, CBMS Regional Conf. Series, no. 29, Amer. Math. Soc., Providence, R. I., 1977.
- [WE4] A. Weinstein, The symplectic "category, " Proc. Conf. Differential Geometric Methods in Mathematical Physics (Clausthal-Zellerfeld, 1980) (in preparation).Zentralblatt MATH: 0486.58017
- [WL] H. Weyl, The classical groups, Princeton Univ. Press, Princeton, N. J., 1946.
American Mathematical Society

- You have access to this content.
- You have partial access to this content.
- You do not have access to this content.
More like this
- Symplectic geometry of rationally connected threefolds
Tian, Zhiyu, Duke Mathematical Journal, 2012 - Symplectic Geometry and Hilbert's Fourth Problem
Álvarez Paiva, J.C., Journal of Differential Geometry, 2005 - Cosphere bundle reduction in contact geometry
Drăgulete, Oanu, Ornea, Liviu, and Ratiu, Tudor S., Journal of Symplectic Geometry, 2003
- Symplectic geometry of rationally connected threefolds
Tian, Zhiyu, Duke Mathematical Journal, 2012 - Symplectic Geometry and Hilbert's Fourth Problem
Álvarez Paiva, J.C., Journal of Differential Geometry, 2005 - Cosphere bundle reduction in contact geometry
Drăgulete, Oanu, Ornea, Liviu, and Ratiu, Tudor S., Journal of Symplectic Geometry, 2003 - The Symplectic Geometry of Penrose Rhombus Tilings
Battaglia, Fiammetta and Prato, Elisa, Journal of Symplectic Geometry, 2008 - Symplectic spectral geometry of semiclassical operators
Pelayo, Álvaro, Bulletin of the Belgian Mathematical Society - Simon Stevin, 2013 - Wong's equations in Poisson geometry
Maspfuhl, Oliver, Journal of Symplectic Geometry, 2004 - The Geometry of Partial Differential Hamiltonian Systems
Vitagliano, Luca, , 2010 - Quasi-Hamiltonian geometry of meromorphic connections
Boalch, Philip, Duke Mathematical Journal, 2007 - Categorified symplectic geometry and the string Lie
2-algebra
Baez, John C. and Rogers, Christopher L., Homology, Homotopy and Applications, 2010 - The Hamiltonian geometry of the space of unitary connections with symplectic curvature
Fine, Joel, Journal of Symplectic Geometry, 2014
