Geodesic
A criterion for a Poisson matrix determinant to be a partial integral of the Hamiltonian system
Russian journal of nonlinear dynamics, Tome 3 (2007) no. 1, pp. 75-80

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

Consider a Hamiltonian system, restricted onto an invariant surface. Does it have an integral, which may be explicitly expressed through the equations, determining this submanifold? A simple criterion of the existence of partial integral, equal to their Poisson matrix determinant, has been found. This integral is not trivial iff the induced Poisson structure is nondegenerate at least at one point. Particularly, the submanifold is to be even-dimensional.
Keywords: Hamiltonian system, partial integral, invariant submanifold. 
@article{ND_2007_3_1_a4,
     author = {D. B. Zotev},
     title = {A criterion for a {Poisson} matrix determinant to be a partial integral of the {Hamiltonian} system},
     journal = {Russian journal of nonlinear dynamics},
     pages = {75--80},
     publisher = {mathdoc},
     volume = {3},
     number = {1},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2007_3_1_a4/}
}
TY  - JOUR
AU  - D. B. Zotev
TI  - A criterion for a Poisson matrix determinant to be a partial integral of the Hamiltonian system
JO  - Russian journal of nonlinear dynamics
PY  - 2007
SP  - 75
EP  - 80
VL  - 3
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2007_3_1_a4/
LA  - ru
ID  - ND_2007_3_1_a4
ER  - 
%0 Journal Article
%A D. B. Zotev
%T A criterion for a Poisson matrix determinant to be a partial integral of the Hamiltonian system
%J Russian journal of nonlinear dynamics
%D 2007
%P 75-80
%V 3
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2007_3_1_a4/
%G ru
%F ND_2007_3_1_a4
D. B. Zotev. A criterion for a Poisson matrix determinant to be a partial integral of the Hamiltonian system. Russian journal of nonlinear dynamics, Tome 3 (2007) no. 1, pp. 75-80. http://geodesic.mathdoc.fr/item/ND_2007_3_1_a4/