|
Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Retrieve article in:
PDF
Book Information
Author(s):
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.,
$69.95,
ISBN 0-8176-4307-9
References:
- 1.
- N. Aronszajn, ``Subcartesian and subriemannian spaces'', Notices A.M.S. 14 (1967) 111.
- 2.
- J.M. Arms, ``Reduction of Poisson algebras at nonzero momentum values'', J. Geom. Phys. 21 (1996) 81-95. MR 1421256 (98a:58063)
- 3.
- J.M. Arms, M. Gotay and G. Jennings, ``Geometric and algebraic reduction for singular momentum maps'', Adv. Math. 79 (1990) 43-103. MR 1031826 (91a:58051)
- 4.
- P.G. Bergmann and I. Goldberg, ``Dirac bracket transformations in phase space'', Phys. Rev. 98 (1955) 531-538. MR 0074314 (17:565a)
- 5.
- E. Bierstone, ``Lifting isotopies from orbit spaces'', Topology 14 (1975) 245-252. MR 0375356 (51:11551)
- 6.
- R. Cushman, ``Reduction, Brouwer's Hamiltonian and the critical inclination'', Celest. Mech. 31 (1983) 401-429. MR 0737806 (85i:70015)
- 7.
- R. Cushman and J. Sniatycki, ``Differential structure of orbit spaces'', Canad. J. Math. 53 (2001) 715-755. MR 1848504 (2002j:53109)
- 8.
- P.A.M. Dirac, ``Generalized Hamiltonian dynamics'', Canad. J. Math. 2 (1950) 129-148. MR 0043724 (13:306b)
- 9.
- A. Friedman, Generalized Functions and Partial Differential Equations, Prentice Hall, Inc., Englewood Cliffs, N.J., 1963. MR 0165388 (29:2672)
- 10.
- V.W. Guillemin and S. Sternberg, ``Geometric quantization and multiplicities of group representations'', Invent. Math. 67 (1982) 515-538. MR 0664118 (83m:58040)
- 11.
- A. Hanson, T. Regge and C. Teitelboim, Constrained Hamiltonian Systems, Accad. Nazionale dei Lincei, Rome, 1976.
- 12.
- H. Künzle, ``Degenerate Lagrangian systems'', Ann. Inst. H. Poincaré 11 (1969) 393-414. MR 0278586 (43:4316)
- 13.
- A. Lichnerowicz, ``Variété symplectique et dynamique associée à une sous-variété'', C.R. Acad. Sci. Paris, Sér. A 280 (1975) 523-527. MR 0405503 (53:9296)
- 14.
- J.E. Marsden and A. Weinstein, ``Reduction of symplectic manifolds with symmetry'', Rep. Math. Phys. 5 (1974) 121-130. MR 0402819 (53:6633)
- 15.
- E. Meinrenken and R. Sjamaar, ``Singular reduction and quantization'', Topology 38 (1999) 699-762. MR 1679797 (2000f:53114)
- 16.
- J.-P. Ortega, Symmetry, Reduction and Stability in Hamiltonian Systems, Ph.D. Thesis, University of California, Santa Cruz, 1998.
- 17.
- R. Palais, ``On the existence of slices for actions of non-compact Lie groups'', Ann. Math. 73 (1961) 295-323. MR 0126506 (23:A3802)
- 18.
- G.W. Schwarz, ``Smooth functions invariant under the action of a compact Lie group'', Topology 14 (1975) 63-68. MR 0370643 (51:6870)
- 19.
- R. Sikorski, Wstep do Geometrii Rózniczkowej, PWN, Warszawa, 1972.
- 20.
- J. Sniatycki, ``Dirac brackets in geometric dynamics'', Ann. Inst. Henri Poincaré 20 (1974) 365-372. MR 0358860 (50:11319)
- 21.
- J. Sniatycki, ``Orbits of families of vector fields on subcartesian spaces'', Ann. Inst. Fourier (Grenoble) 53 (2003) 2257-2296. MR 2044173
- 22.
- J. Sniatycki and A. Weinstein, ``Reduction and quantization for singular momentum mappings'', Lett. Math. Phys. 7 (1983) 155-161. MR 0708438 (85c:58046)
- 23.
- P. Stefan, ``Accessible sets, orbits and foliations with singularities'', Proc. London Math. Soc. 29 (1974) 699-713. MR 0362395 (50:14837)
- 24.
- W.M. Tulczyjew, unpublished lectures, Institute of Theoretical Physics, Warsaw University, 1967.
- 25.
- H. Weyl, The Classical Groups (2nd ed.), Princeton University Press, Princeton, 1946. MR 1488158 (98k:01049)
Additional Information:
Reviewer(s):
Jedrzej
Sniatycki
Affiliation:
University of Calgary
Email:
sniat@math.ucalgary.ca
Review Information:
Journal:
Bull. Amer. Math. Soc.
42
(2005),
215-223.
MSC
(2000):
Primary 37J15, 53D20
PII:
S 0273-0979(04)01039-0
Posted:
November 29, 2004
Copyright of article:
Copyright
2004,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
|
