Geodesic
To the calculation of the mapping degree of finite dimensional vector field
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 67-73

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

In this paper we propose and justify a new method calculation of the mapping degree of $n$-dimensional vector field on the unit sphere of the space $\mathrm{R}^n$, $n\geq 2$. The essence of the proposed method is that the calculation of the mapping degree of vector field is reduced to the calculation of the mapping degree of its tangent component on the components of the set, where the vector field has an obtuse angle with the unit vector field. In the special case, for the gradient of a smooth positively homogeneous function, we derive a formula for calculation of the mapping degree through the Eulerian characteristic of the set of points where the function is negative.
Keywords: vector field, mapping degree of vector field, positive homogeneous function, Eulerian characteristic. 
@article{IVM_2023_6_a5,
     author = {E. Mukhamadiev and A. N. Naimov},
     title = {To the calculation of the mapping degree of finite dimensional vector field},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {67--73},
     publisher = {mathdoc},
     number = {6},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_6_a5/}
}
TY  - JOUR
AU  - E. Mukhamadiev
AU  - A. N. Naimov
TI  - To the calculation of the mapping degree of finite dimensional vector field
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 67
EP  - 73
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_6_a5/
LA  - ru
ID  - IVM_2023_6_a5
ER  - 
%0 Journal Article
%A E. Mukhamadiev
%A A. N. Naimov
%T To the calculation of the mapping degree of finite dimensional vector field
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 67-73
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_6_a5/
%G ru
%F IVM_2023_6_a5
E. Mukhamadiev; A. N. Naimov. To the calculation of the mapping degree of finite dimensional vector field. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2023), pp. 67-73. http://geodesic.mathdoc.fr/item/IVM_2023_6_a5/