Geodesic
Sufficient conditions for the existence of a center in a second-order nonlinear dynamical system in a critical case
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 51-62

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

We study an autonomous nonlinear system of second-order differential equations whose linear approximation matrix has a pair of purely imaginary eigenvalues and whose nonlinear part can be represented as the sum of forms of order ${\geqslant}2$ with respect to the components of the phase vector. We obtain sufficient conditions for the existence of a center or focus in a neighborhood of the zero solution.
Keywords: differential equation, critical case, complex focus, center, distinguishing between center and focus. 
@article{INTO_2022_217_a6,
     author = {E. Yu. Liskina},
     title = {Sufficient conditions for the existence of a center in a second-order nonlinear dynamical system in a critical case},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {51--62},
     publisher = {mathdoc},
     volume = {217},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_217_a6/}
}
TY  - JOUR
AU  - E. Yu. Liskina
TI  - Sufficient conditions for the existence of a center in a second-order nonlinear dynamical system in a critical case
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 51
EP  - 62
VL  - 217
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_217_a6/
LA  - ru
ID  - INTO_2022_217_a6
ER  - 
%0 Journal Article
%A E. Yu. Liskina
%T Sufficient conditions for the existence of a center in a second-order nonlinear dynamical system in a critical case
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 51-62
%V 217
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_217_a6/
%G ru
%F INTO_2022_217_a6
E. Yu. Liskina. Sufficient conditions for the existence of a center in a second-order nonlinear dynamical system in a critical case. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 51-62. http://geodesic.mathdoc.fr/item/INTO_2022_217_a6/