Singularities of Poisson and Nambu structures
Dufour, Jean-Paul
Banach Center Publications, Tome 51 (2000), p. 61-68 / Harvested from The Polish Digital Mathematics Library
Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:209044
@article{bwmeta1.element.bwnjournal-article-bcpv51z1p61bwm,
     author = {Dufour, Jean-Paul},
     title = {Singularities of Poisson and Nambu structures},
     journal = {Banach Center Publications},
     volume = {51},
     year = {2000},
     pages = {61-68},
     zbl = {1032.53071},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p61bwm}
}
Dufour, Jean-Paul. Singularities of Poisson and Nambu structures. Banach Center Publications, Tome 51 (2000) pp. 61-68. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv51z1p61bwm/

[000] [A-G] D. Alekseevsky and P. Guha, On decomposability of Nambu-Poisson tensor, preprint Max-Planck-Institut für Mathematik, MPI/96-9, 1996.

[001] [A-C-L] D. Arnal, M. Cahen and J. Ludwig, Lie groups whose coadjoint orbits are of dimension smaller than two, Letters in Math. Phys. 33 (1995), 183-186. | Zbl 0839.22005

[002] [A] V. I. Arnol'd, Geometrical methods in the theory of differential equations, 2nd edition Grundlehren der mathematischen, Springer Verlag (1988).

[003] [A-I] V. I. Arnol'd and Yu. S. Il'yashenko, Ordinary differential equations, Dynamical Systems I, Encyclopaedia of Mathematical Sciences, Springer Verlag (1988).

[004] [C-LN] C. Camacho and A. Lins Neto, The topology of integrable forms near a singularity, Pub. math. I.H.E.S. 55 (1982), 5-32. | Zbl 0505.58026

[005] [C-C] F. Cano and D. Cerveau, Book in preparation.

[006] [D] J. P. Dufour, Quadratisation de structures de Poisson, Séminaire Gaston Darboux, Montpellier (1992).

[007] [D-H] J. P. Dufour and A. Haraki, Rotationnel et structures de Poisson quadratiques, C. R. Acad. Sci. Paris 312 I (1991), 137-140.

[008] [D-N] J. P. Dufour and T. Z. Nguyen, Linearization of Nambu structures, to appear in Compositio Mathematica. | Zbl 0969.53047

[009] [D-Z] J. P. Dufour and M. Zhitomirskii, Singularities and bifurcations of 3-dimensional Poisson structures, preprint. | Zbl 0992.37049

[010] [G] Ph. Gautheron, Some remarks concerning Nambu mechanics, Lett. Math. Phys. 37 (1996), 103-116. | Zbl 0849.70014

[011] [K] J. L. Koszul, Crochets de Schouten-Nijenhuis et cohomologie, Astérisque (hors série) 127 bis (1985), 257-271.

[012] [KS] Y. Kosmann-Schwarzbach, Exact Gerstenhaber algebras and Lie bialgebroids, Acta Applicandae Mathematicae 41 (1995), 153-165. | Zbl 0837.17014

[013] [Ku] I. Kupka, The singularities of integrable structurally stable Pfaffian forms, Proc. Nat. Acad. Sci. USA 52 (1964), 1431-1432. | Zbl 0137.41404

[014] [M-V-V] G. Marmo, G. Vilasi and A. M. Vinogradov, The local structure of n-Poisson and n-Jacobi manifolds, J. of Geom. and Phys. 25 (1998), 141-182. | Zbl 0978.53126

[015] [Ma] J. Martinet, Normalisation des champs de vecteurs holomorphes (d'après A. D. Brujno), Séminaire Bourbaki, 564 (1980-1981).

[016] [Me] A. Medeiros, Structural stability of integrable differential forms, Lecture Notes in Math. 597 (1977), 395-428.

[017] [N] N. Nakanishi, On Nambu-Poisson manifolds, Reviews in Math. Phys. 10 (1998), 499-510. | Zbl 0929.70015

[018] [Na] Y. Nambu, Generalized Hamiltonian dynamics, Phys. Rev. D7 (1973), 2405-2412. | Zbl 1027.70503

[019] [T] L. Takhtajan, On foundation of the generalized Nambu mechanics, Comm. Math. Phys. 160 (1994), 295-315. | Zbl 0808.70015

[020] [W] A. Weinstein, The modular automorphism group of a Poisson manifold, preprint (May 1996).

[021] [W-R] W. T. Wu and G. Reeb, Sur les espaces fibrés et les variétés feuilletées, Actualités Scientifiques et Industrielles N. 1183, Publications de l'Institut de Mathématiques de Strasbourg XI, Paris, Hermann, 1952.