Geodesic
Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution
Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 69-90

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper presents a method for checking completeness of families of functions which are in involution with respect to compatible Poisson brackets. Several examples of compatible Poisson brackets on duals of Lie algebras are considered, as well as the associated involutive function families and Hamiltonian systems. The transitions of Liouville tori for some nonintegrable Hamiltonian systems, notably the equations of motion for a higher dimensional rigid body, are described. 
@article{IM2_1992_38_1_a2,
     author = {A. V. Bolsinov},
     title = {Compatible {Poisson} brackets on {Lie} algebras and completeness of families of functions in involution},
     journal = {Izvestiya. Mathematics },
     pages = {69--90},
     publisher = {mathdoc},
     volume = {38},
     number = {1},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a2/}
}
TY  - JOUR
AU  - A. V. Bolsinov
TI  - Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution
JO  - Izvestiya. Mathematics 
PY  - 1992
SP  - 69
EP  - 90
VL  - 38
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a2/
LA  - en
ID  - IM2_1992_38_1_a2
ER  - 
%0 Journal Article
%A A. V. Bolsinov
%T Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution
%J Izvestiya. Mathematics 
%D 1992
%P 69-90
%V 38
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a2/
%G en
%F IM2_1992_38_1_a2
A. V. Bolsinov. Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution. Izvestiya. Mathematics , Tome 38 (1992) no. 1, pp. 69-90. http://geodesic.mathdoc.fr/item/IM2_1992_38_1_a2/