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. 
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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/

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