Normal forms of vector fields on Poisson manifolds

Philippe Monnier[1]; Nguyen Tien Zung[1]

  • [1] Laboratoire Emile Picard Université Paul Sabatier 31062 Toulouse Cedex *9 FRANCE

Annales mathématiques Blaise Pascal (2006)

  • Volume: 13, Issue: 2, page 349-380
  • ISSN: 1259-1734

Abstract

top
We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.

How to cite

top

Monnier, Philippe, and Zung, Nguyen Tien. "Normal forms of vector fields on Poisson manifolds." Annales mathématiques Blaise Pascal 13.2 (2006): 349-380. <http://eudml.org/doc/10534>.

@article{Monnier2006,
abstract = {We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.},
affiliation = {Laboratoire Emile Picard Université Paul Sabatier 31062 Toulouse Cedex *9 FRANCE; Laboratoire Emile Picard Université Paul Sabatier 31062 Toulouse Cedex *9 FRANCE},
author = {Monnier, Philippe, Zung, Nguyen Tien},
journal = {Annales mathématiques Blaise Pascal},
keywords = {normal forms; Hamiltonian vector fields; Jacobi structures; homogeneous Poisson structures},
language = {eng},
month = {7},
number = {2},
pages = {349-380},
publisher = {Annales mathématiques Blaise Pascal},
title = {Normal forms of vector fields on Poisson manifolds},
url = {http://eudml.org/doc/10534},
volume = {13},
year = {2006},
}

TY - JOUR
AU - Monnier, Philippe
AU - Zung, Nguyen Tien
TI - Normal forms of vector fields on Poisson manifolds
JO - Annales mathématiques Blaise Pascal
DA - 2006/7//
PB - Annales mathématiques Blaise Pascal
VL - 13
IS - 2
SP - 349
EP - 380
AB - We study formal and analytic normal forms of radial and Hamiltonian vector fields on Poisson manifolds near a singular point.
LA - eng
KW - normal forms; Hamiltonian vector fields; Jacobi structures; homogeneous Poisson structures
UR - http://eudml.org/doc/10534
ER -

References

top
  1. G.D. Birkhoff, Dynamical Systems, (1927), AMS Colloq. Publ., Providence Zbl53.0732.01
  2. A.D. Bruno, Analytic form of differential equations, Trans. Moscow Math. Soc. 25 (1971), 131-288 Zbl0272.34018
  3. A.D. Bruno, Local methods in nonlinear differential equations, (1989), Springer-Verlag, Berlin Zbl0674.34002MR993771
  4. J. Conn, Normal forms for analytic Poisson structures, Ann. of Math. 119 (1984), 577-601 Zbl0553.58004MR744864
  5. P. Dazord, A. Lichnerowicz, Ch.-M. Marle, Structure locale des variétés de Jacobi, J. Math. Pures Appl. 70 (1991), 101-152 Zbl0659.53033MR1091922
  6. J.-P. Dufour, N. T. Zung, Poisson structures and their normal forms, (2005), Birkhauser Verlag, Basel Zbl1082.53078MR2178041
  7. V. Ginzburg, Momentum mappings and Poisson cohomology, Internat. J. Math. 7 (1996), 329-358 Zbl0867.58028MR1395934
  8. A.W. Knapp, Lie groups beyond an introduction, (2002), Birkhauser, Boston Zbl1075.22501MR1920389
  9. E. Miranda, N.T. Zung, Equivariant normal forms of Poisson structures, (2005) Zbl1112.53062
  10. C.L. Siegel, J. Moser, Lectures on celestial mechanics, (1971), Springer-Verlag, New York - Heidelberg Zbl0817.70001MR502448
  11. I. Vaisman, Lectures on the Geometry of Poisson Manifolds, (1994), Birkhauser Verlag, Basel Zbl0810.53019MR1269545
  12. A. Weinstein, The local structure of Poisson manifolds, J. Differential Geom. 18 (1983), 523-557 Zbl0524.58011MR723816
  13. N.T. Zung, Convergence versus integrability in Poincaré-Dulac normal forms, Math. Res. Lett. 9 (2002), 217-228 Zbl1019.34084MR1909639
  14. N.T. Zung, Torus action and integrable systems, (2004) 
  15. N.T. Zung, Convergence versus integrability in Birkhoff normal forms, Ann. of Math. 161 (2005), 139-154 Zbl1076.37045MR2150385

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.