Skip to Main Content

Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Authors: J.-P. Ortega and T. S. Ratiu
Title: Momentum maps and Hamiltonian reduction
Additional book information: Progress in Math., vol. 222, Birkhäuser Boston, Inc., Boston, MA, 2004, xxxiv + 497 pp., ISBN 0-8176-4307-9, $69.95$

References [Enhancements On Off] (What's this?)

1.
N. Aronszajn, ``Subcartesian and subriemannian spaces'', Notices A.M.S. 14 (1967) 111.
  • Judith Arms, Reduction of Poisson algebras at nonzero momentum values, J. Geom. Phys. 21 (1996), no. 1, 81–95. MR 1421256, DOI 10.1016/S0393-0440(96)00009-5
  • Judith M. Arms, Mark J. Gotay, and George Jennings, Geometric and algebraic reduction for singular momentum maps, Adv. Math. 79 (1990), no. 1, 43–103. MR 1031826, DOI 10.1016/0001-8708(90)90058-U
  • Peter G. Bergmann and Irwin Goldberg, Dirac bracket transformations in phase space, Phys. Rev. (2) 98 (1955), 531–538. MR 74314
  • Edward Bierstone, Lifting isotopies from orbit spaces, Topology 14 (1975), no. 3, 245–252. MR 375356, DOI 10.1016/0040-9383(75)90005-1
  • Richard Cushman, Reduction, Brouwer’s Hamiltonian, and the critical inclination, Celestial Mech. 31 (1983), no. 4, 401–429. MR 737806, DOI 10.1007/BF01230294
  • Richard Cushman and Jȩdrzej Śniatycki, Differential structure of orbit spaces, Canad. J. Math. 53 (2001), no. 4, 715–755. MR 1848504, DOI 10.4153/CJM-2001-029-1
  • P. A. M. Dirac, Generalized Hamiltonian dynamics, Canad. J. Math. 2 (1950), 129–148. MR 43724, DOI 10.4153/cjm-1950-012-1
  • Avner Friedman, Generalized functions and partial differential equations, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0165388
  • V. Guillemin and S. Sternberg, Geometric quantization and multiplicities of group representations, Invent. Math. 67 (1982), no. 3, 515–538. MR 664118, DOI 10.1007/BF01398934
  • 11.
    A. Hanson, T. Regge and C. Teitelboim, Constrained Hamiltonian Systems, Accad. Nazionale dei Lincei, Rome, 1976.
  • H. P. Künzle, Degenerate Lagrangian systems, Ann. Inst. H. Poincaré Sect. A (N.S.) 11 (1969), 393–414 (English, with French summary). MR 278586
  • André Lichnerowicz, Variété symplectique et dynamique associée à une sous-variété, C. R. Acad. Sci. Paris Sér. A-B 280 (1975), A523–A527. MR 405503
  • Jerrold Marsden and Alan Weinstein, Reduction of symplectic manifolds with symmetry, Rep. Mathematical Phys. 5 (1974), no. 1, 121–130. MR 402819, DOI 10.1016/0034-4877(74)90021-4
  • Eckhard Meinrenken and Reyer Sjamaar, Singular reduction and quantization, Topology 38 (1999), no. 4, 699–762. MR 1679797, DOI 10.1016/S0040-9383(98)00012-3
  • 16.
    J.-P. Ortega, Symmetry, Reduction and Stability in Hamiltonian Systems, Ph.D. Thesis, University of California, Santa Cruz, 1998.
  • Richard S. Palais, On the existence of slices for actions of non-compact Lie groups, Ann. of Math. (2) 73 (1961), 295–323. MR 126506, DOI 10.2307/1970335
  • Gerald W. Schwarz, Smooth functions invariant under the action of a compact Lie group, Topology 14 (1975), 63–68. MR 370643, DOI 10.1016/0040-9383(75)90036-1
  • 19.
    R. Sikorski, Wstep do Geometrii Rózniczkowej, PWN, Warszawa, 1972.
  • Jędrzej Śniatycki, Dirac brackets in geometric dynamics, Ann. Inst. H. Poincaré Sect. A (N.S.) 20 (1974), 365–372. MR 358860
  • Jȩdrzej Śniatycki, Orbits of families of vector fields on subcartesian spaces, Ann. Inst. Fourier (Grenoble) 53 (2003), no. 7, 2257–2296 (English, with English and French summaries). MR 2044173
  • Jędrzej Śniatycki and Alan Weinstein, Reduction and quantization for singular momentum mappings, Lett. Math. Phys. 7 (1983), no. 2, 155–161. MR 708438, DOI 10.1007/BF00419934
  • P. Stefan, Accessible sets, orbits, and foliations with singularities, Proc. London Math. Soc. (3) 29 (1974), 699–713. MR 362395, DOI 10.1112/plms/s3-29.4.699
  • 24.
    W.M. Tulczyjew, unpublished lectures, Institute of Theoretical Physics, Warsaw University, 1967.
  • Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR 1488158

  • Review Information:

    Reviewer: Jȩdrzej Śniatycki
    Affiliation: University of Calgary
    Email: sniat@math.ucalgary.ca
    Journal: Bull. Amer. Math. Soc. 42 (2005), 215-223
    Published electronically: November 29, 2004
    Review copyright: © Copyright 2004 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.