Geodesic
Phase flows and vector Hamiltonians
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2011), pp. 3-9.

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

We present generalization of the Nambu mechanics on the base of Liouville theorem. We prove that Poisson structure of $n$-dimensional multi-symplectic phase space is induced by $(n-1)$ Hamilton $k$-vectors fields. Each of these fields requires introduction of $k$-hamiltonians.
Mots-clés : Liouville theorem
Keywords: Hamilton vectors fields. 
@article{IVM_2011_3_a0,
     author = {V. N. Dumachev},
     title = {Phase flows and vector {Hamiltonians}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--9},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_3_a0/}
}
TY  - JOUR
AU  - V. N. Dumachev
TI  - Phase flows and vector Hamiltonians
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2011
SP  - 3
EP  - 9
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2011_3_a0/
LA  - ru
ID  - IVM_2011_3_a0
ER  - 
%0 Journal Article
%A V. N. Dumachev
%T Phase flows and vector Hamiltonians
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2011
%P 3-9
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2011_3_a0/
%G ru
%F IVM_2011_3_a0
V. N. Dumachev. Phase flows and vector Hamiltonians. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 3 (2011), pp. 3-9. http://geodesic.mathdoc.fr/item/IVM_2011_3_a0/

[1] Griffits F., Vneshnie differentsialnye sistemy i variatsionnoe ischislenie, Mir, M., 1983 | MR

[2] Ishii M., “Painleve property and algebraic integrability of single variable ordinary differential equations with dominants”, Progr. Theor. Phys., 84 (1990), 386–391 | DOI | MR | Zbl

[3] Nambu Y., “Generalized Hamiltonian dynamics”, Phys. Rev. D, 7 (1973), 2405–2412 | DOI | MR | Zbl

[4] Fujii K., A new algebraic structure of finite quantum systems and the modified Bessel functions, arXiv: 0704.1844 | MR