Normal forms of symplectic structures on the stratified spaces

W. Domitrz; S. Janeczko

Colloquium Mathematicae (1995)

  • Volume: 68, Issue: 1, page 101-119
  • ISSN: 0010-1354

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Domitrz, W., and Janeczko, S.. "Normal forms of symplectic structures on the stratified spaces." Colloquium Mathematicae 68.1 (1995): 101-119. <http://eudml.org/doc/210284>.

@article{Domitrz1995,
author = {Domitrz, W., Janeczko, S.},
journal = {Colloquium Mathematicae},
keywords = {symplectic structures; stratified spaces; germs; bicharacteristics; Darboux form},
language = {eng},
number = {1},
pages = {101-119},
title = {Normal forms of symplectic structures on the stratified spaces},
url = {http://eudml.org/doc/210284},
volume = {68},
year = {1995},
}

TY - JOUR
AU - Domitrz, W.
AU - Janeczko, S.
TI - Normal forms of symplectic structures on the stratified spaces
JO - Colloquium Mathematicae
PY - 1995
VL - 68
IS - 1
SP - 101
EP - 119
LA - eng
KW - symplectic structures; stratified spaces; germs; bicharacteristics; Darboux form
UR - http://eudml.org/doc/210284
ER -

References

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  1. [1] R. Abraham and J. Marsden, Foundations of Mechanics, 2nd ed., Benjamin/Cummings, Reading, 1978. Zbl0393.70001
  2. [2] V. I. Arnold, Ordinary Differential Equations, The MIT Press, Cambridge, 1978. 
  3. [3] V. I. Arnold, Lagrangian manifolds with singularities, asymptotic rays and the open swallowtail, Functional Anal. Appl. 15 (1981), 235-246. 
  4. [4] M. Golubitsky and D. Tischler, An example of moduli for singular symplectic forms, Invent. Math. 38 (1977), 219-225. Zbl0345.58002
  5. [5] M. Golubitsky and D. Tischler, On local stability of differential forms, Trans. Amer. Math. Soc. 223 (1976), 205-221. Zbl0339.58003
  6. [6] V. Guillemin and S. Sternberg, Symplectic Techniques in Physics, Cambridge Univ. Press, Cambridge, 1984. Zbl0576.58012
  7. [7] S. Janeczko, Generalized Luneburg canonical varieties and vector fields on quasicaustics, J. Math. Phys. 31 (4) (1990), 997-1009. Zbl0714.58051
  8. [8] S. Janeczko, Coisotropic varietes and their generating families, Ann. Inst. H. Poincaré 56 (4) (1992), 429-441. Zbl0812.53036
  9. [9] S. Janeczko and I. Stewart, Symplectic singularities and optical diffraction, in: Lecture Notes in Math. 1493, Springer, 1991, 220-255. Zbl0742.58020
  10. [10] E. Lerman, R. Montgomery and R. Sjamaar, Examples of singular reduction, preprint, 1991. Zbl0812.58034
  11. [11] J. Martinet, Sur les singularités des formes différentielles, Ann. Inst. Fourier (Grenoble) 20 (1) (1970), 95-178. Zbl0189.10001
  12. [12] --, Singularities of Smooth Functions and Maps, Cambridge Univ. Press, Cambridge, 1982. 
  13. [13] J. Moser, On volume elements on manifolds, Trans. Amer. Math. Soc. 120 (1965), 280-296. 
  14. [14] R. Roussarie, Modèles locaux de champs et de formes, Astérisque 30 (1975), 1-181. Zbl0327.57017
  15. [15] R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction, Ann. of Math. 134 (1991), 375-422. Zbl0759.58019
  16. [16] A. Weinstein, Lectures on Symplectic Manifolds, CBMS Conf. Ser. in Math. 29, Amer. Math. Soc., Providence, R.I., 1977. 

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