Geodesic
Integral Formula for a Generalized Sato--Levine Invariant in Magnetic Hydrodynamics
Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 524-537

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

For a pair of divergence-free vector fields $\mathbf B$ and $\widetilde{\mathbf B}$ respectively localized in two oriented tubes $U$ and $\widetilde U$ in $\mathbb R^3$, we propose a fourth-order integral $W$ and describe the dependence between the integral $W$ and a higher topological invariant $\beta=\beta(l,\widetilde l)$ (namely, the generalized Sato–Levine invariant). The new integral is a generalization of the well-known integral, which was defined earlier for two tubes with zero linking number.
Keywords: topological invariant, oriented magnetic tube, linking number, magnetic hydrodynamics, Lie derivative, Massey product, gradient field.
Mots-clés : Sato–Levine invariant 
@article{MZM_2009_85_4_a3,
     author = {P. M. Akhmet'ev and O. V. Kunakovskaya},
     title = {Integral {Formula} for a {Generalized} {Sato--Levine} {Invariant} in {Magnetic} {Hydrodynamics}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {524--537},
     publisher = {mathdoc},
     volume = {85},
     number = {4},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a3/}
}
TY  - JOUR
AU  - P. M. Akhmet'ev
AU  - O. V. Kunakovskaya
TI  - Integral Formula for a Generalized Sato--Levine Invariant in Magnetic Hydrodynamics
JO  - Matematičeskie zametki
PY  - 2009
SP  - 524
EP  - 537
VL  - 85
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a3/
LA  - ru
ID  - MZM_2009_85_4_a3
ER  - 
%0 Journal Article
%A P. M. Akhmet'ev
%A O. V. Kunakovskaya
%T Integral Formula for a Generalized Sato--Levine Invariant in Magnetic Hydrodynamics
%J Matematičeskie zametki
%D 2009
%P 524-537
%V 85
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a3/
%G ru
%F MZM_2009_85_4_a3
P. M. Akhmet'ev; O. V. Kunakovskaya. Integral Formula for a Generalized Sato--Levine Invariant in Magnetic Hydrodynamics. Matematičeskie zametki, Tome 85 (2009) no. 4, pp. 524-537. http://geodesic.mathdoc.fr/item/MZM_2009_85_4_a3/