Powiadomienia systemowe
- Sesja wygasła!
- Sesja wygasła!
- Sesja wygasła!
Tytuł artykułu
Autorzy
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
We show that the space P/G of orbits of a proper action of a Lie group G on a locally compact differential space P is a locally compact differential space with quotient topology. Applying this result to reduction of symmetries of Hamiltonian systems, we prove the reduction by stages theorem.
Wydawca
Czasopismo
Rocznik
Tom
Strony
192--210
Opis fizyczny
Bibliogr. 21 poz.
Twórcy
autor
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada
autor
- Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada
Bibliografia
- [1] R. Abraham, J. Robbin, Transversal Mappings and Flows, Academic Press, New York, 1967.
- [2] E. Bierstone, The Structure of Orbit Spaces and the Singularities of Equivariant Mappings, Monografias de Matemática, vol. 35, Instituto de Matemática Pura e Applicada, Rio de Janeiro, 1980.
- [3] K. Buchner, M. Heller, P. Multarzynski, W. Sasin, Literature on differential spaces, Acta Cosmologica 19 (1993), 111–129.
- [4] R. Cushman, Reduction, Brouwer’s Hamiltonian and the critical inclination, Celestial Mech. Dynam. Astronom. 31 (1983), 401–429.
- [5] R. H. Cushman, L. M. Bates, Global Aspects of Classical Integrable Systems, Birkhäuser, Basel, 1997.
- [6] R. Cushman, J. J. Duistermaat, J. Śniatycki, Geometry of Nonholonomically Constrained Systems, World Scientific, Singapore, 2010.
- [7] R. Cushman, J. Sniatycki, Differential structure of orbit spaces, Canad. J. Math. 53 (2001), 235–248.
- [8] J. L. Kelley, General Topology, Van Nostrand, New York, 1955, reprinted by Springer Verlag, New York.
- [9] P. Libermann, C-M. Marle, Symplectic Geometry and Analytical Mechanics, Translated from the French by Bertram Eugene Schwarzbach. Mathematics and its Applications, 35. D. Reidel Publishing Co., Dordrecht, 1987.
- [10] T. Lusala, J. Sniatycki, Stratified subcartesian spaces, Canadian Math. Bulletin, (to appear).
- [11] J. E. Marsden, G. Misiołek, J.-P. Ortega, M. Perlmutter, T. Ratiu, Hamiltonian Reduction by Stages, Lecture Notes in Mathematics, vol. 1913, Springer, Berlin, Heidelberg, 2007.
- [12] J. N. Mather, Stratificationa and mappings, in: Dynamical Systems (M. M. Peixoto, ed.), Academic Press, 1973, 195–232.
- [13] J.-P. Ortega, T. S. Ratiu, Momentum Maps and Hamiltonian Reduction, Birkhäuser, Boston, 2004.
- [14] R. S. Palais, On the existence of slices for actions of non-compact Lie groups, Ann. Math. 73 (1961), 295–323.
- [15] Z. Pasternak-Winiarski, On some differential structures defined by actions of groups, Conference on Differential Geometry and its Applications, Nové Mesto na Morave, Czechoslovakia, September 5–9, 1983. Proceedings, pp. 105–115, Charles University, Prague, 1984.
- [16] G. Schwarz, Smooth functions invariant under the action of compact Lie groups, Topology 14 (1975), 63–68.
- [17] R. Sikorski, Wstęp do Geometrii Różniczkowej, PWN, Warszawa, 1972.
- [18] J. Śniatycki, Integral curves of derivations on locally semi-algebraic differential spaces, Dynamical Systems and Differential Equations, (Proceedings of the Fourth International Conference on Dynamical Systems and Differential Equations, May 24–27, 2002, Wilmington, NC, USA), W. Feng, S. Hu and X. Lu (Editors), American Institute of Mathematical Sciences Press, Springfield MO. 2003, pp. 825–831.
- [19] J. Śniatycki, Orbits of families of vector fields on subcartesian spaces, Ann. Inst. Fourier (Grenoble) 53 (2003), 2257–2296.
- [20] J. Śniatycki, Differential Geometry of Singular Spaces and Reduction of Symmetry, Cambridge University Press (to appear).
- [21] H. Weyl, The Classical Groups (2nd. edition), Princeton University Press, Princeton, 1946.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-ac995bf9-d9cd-4852-a135-55828d81ed57