Geodesic
On the calculation of index of a vector field
Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 44-54 
P. P. Zabreiko; A. V. Krivko-Krasko. On the calculation of index of a vector field. Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 44-54. http://geodesic.mathdoc.fr/item/TIMB_2016_24_2_a5/
@article{TIMB_2016_24_2_a5,
     author = {P. P. Zabreiko and A. V. Krivko-Krasko},
     title = {On the calculation of index of a vector field},
     journal = {Trudy Instituta matematiki},
     pages = {44--54},
     year = {2016},
     volume = {24},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2016_24_2_a5/}
}
TY  - JOUR
AU  - P. P. Zabreiko
AU  - A. V. Krivko-Krasko
TI  - On the calculation of index of a vector field
JO  - Trudy Instituta matematiki
PY  - 2016
SP  - 44
EP  - 54
VL  - 24
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TIMB_2016_24_2_a5/
LA  - ru
ID  - TIMB_2016_24_2_a5
ER  - 
%0 Journal Article
%A P. P. Zabreiko
%A A. V. Krivko-Krasko
%T On the calculation of index of a vector field
%J Trudy Instituta matematiki
%D 2016
%P 44-54
%V 24
%N 2
%U http://geodesic.mathdoc.fr/item/TIMB_2016_24_2_a5/
%G ru
%F TIMB_2016_24_2_a5

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

In the article, for a plane (and nonhomogeneous!) polynomial vector field, there presents an algorithm of calculation of asymptotical index. Also, it is given a new method of calculating index of finite singular points.

[1] Zabreiko P. P., “O vychislenii indeksa Puankare”, DAN SSSR, 141:5 (1962)

[2] Senchakova N. V., “O vychislenii indeksa Puankare vektornykh polei s odnorodnymi komponentami”, Vestnik Yaroslavskogo universiteta, 1974, no. 8, 103–124

[3] Bokher M., Vvedenie v vysshuyu algebru, Gosudarstvennoe tekhniko-teoreticheskoe izdatelstvo, M.–L., 1933

[4] Gantmakher F. R., Teoriya matrits, Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 2004 | MR

[5] Zabreiko P. P., Senchakova N. V., “O vychislenii indeksa Puankare ploskikh vektornykh polei”, Vestnik Yaroslavskogo universiteta, 1974, no. 8, 38–45

[6] Krasnoselskii M. A., Perov A. I., Povolotskii A. I., Zabreiko P. P., Vektornye polya na ploskosti, Gosudarstvennoe izdatelstvo fiziko-matematicheskoi literatury, 1963 | MR

[7] Krasnoselskii M. A., Vainikko G. M., Zabreiko P. P., Rutitskii Ya. B., Stetsenko V. Ya., Priblizhennoe reshenie operatornykh uravnenii, Nauka, Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1969 | MR

[8] Uoker R., Algebraicheskie krivye, Izdatelstvo inostrannoi literatury, M., 1952 | MR

[9] Chebotarev N. G., Teoriya algebraicheskikh funktsii, Nauka, Glavnaya redaktsiya fiziko-matematicheskoi literatury, M., 1948