A symplectic slice theorem

Letters in Mathematical Physics

Volumn 59, Issue 1, 2002, Pages 81-93

  Ortega, Juan Pablo ^a   Ratiu, Tudor S ^b  

^a INSTITUT NON LINÉAIRE DE NICE   (France)

^b Ecl Polytech Federale ^*  (Switzerland)

Author keywords

Chu map; Momentum map; Reconstruction equations; Slice; Symplectic

Indexed keywords

EID: 0038674152     PISSN: 03779017     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1014407427842     Document Type: Article

References (19)

1. Abraham, R. and Marsden, J. E.: Foundations of Mechanics, 2nd edn, Addison-Wesley, Englewood Cliffs, 1978.
2. Alekseev, A., Malkin, A. and Meinrenken, E.: Lie group valued momentum maps, J. Differential Geom. 48 (1998), 445-495.
3. Bates, L. and Lerman, E.: Proper group actions and symplectic stratified spaces, Pacific J. Math. 181(2) (1997), 201-229.
4. Chu, R. Y.: Symplectic homogeneous spaces, Trans. Amer Math. Soc. 197 (1975), 145-159.
5. Guillemin, V. and Sternberg, S.: A normal form for the moment map, In: S. Sternberg (ed.), Differential Geometric Methods in Mathematical Physics. Math. Phys. Stud. 6, D. Reidel, Dordrecht, 1984.
6. Guillemin, V. and Sternberg, S.: Symplectic Techniques in Physics, Cambridge Univ. Press, 1984.
7. Marle, C-M.: Le voisinage d'une orbite d'une action hamiltonienne d'un groupe de Lie, In: P. Dazord and N. Desolneux-Moulis (eds), Séminaire Sud-Rhodanien de Géométrie II, 1984, pp. 9-35.
8. Marle, C-M.: Modéle d'action hamiltonienne d'un groupe the Lie sur une variété symplectique, Rend. Sem. Mat. Univers. Politecn. Torino 43(2) (1985), 227-251.
9. Marsden, J. E. and Weinstein, A.: Reduction of symplectic manifolds with symmetry, Rep. Math. Phys. 5(1) (1974), 121-130.
10. McDuff, D.: The moment map for circle actions on symplectic manifolds, J. Geom. Phys. 5 (1988), 149-160.
11. Ortega, J.-P.: Symmetry, reduction, and stability in Hamiltonian systems, PhD Thesis. Univ. of California, Santa Cruz, June 1998.
12. Ortega, J.-P.: Singular dual pairs, Preprint.
13. Ortega, J.-P. and Ratiu, T. S.: The optimal momentum map, Preprint.
14. Ortega, J.-P. and Ratiu, T. S.: Hamiltonian singular reduction, To appear in Progr. in Math., Birkhäuser, Basel, 2002.
15. Palais, R.: On the existence of slices for actions of non-compact Lie groups, Ann. Math. 73 (1961), 295-323.
16. Roberts, M., Wulff, C. and Lamb, J. S. W.: Hamiltonian systems near relative equilibria, Preprint, 1999.
17. Sjamaar, R. and Lerman, E.: Stratified symplectic spaces and reduction, Ann. of Math. 134 (1991), 375-422.
18. Scheerer, U. and Wulff, C.: Reduced dynamics for momentum maps with cocycles. CR Acad. Sci. Paris, Série I. To appear.
19. Weinstein, A.: Lectures on Symplectic Manifolds, Expository lectures from the CBMS Regional Conference held at the University of North Carolina, March 8-12, 1976, Regional Conf. Ser. Math. 29, Amer. Math. Soc., Providence, 1976.