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Conference publications

Abstracts

XVI conference

About sufficient conditions for existence the center in one critical case

Liskina E.Y.

S.A. Esenin Ryazan state univercity, Faculty of physic and mathematic, Department of mathematic analisys. Russia, 390000, Ryazan, Svoboda street, 46, 70. Phone: (4912)28-05-88. E-mail: e.liskina@rsu.edu.ru, katelis@yandex.ru

1 pp. (accepted)

In this paper the autonomous non-linear system of the differential equations of the second order is researched. The matrix of linear approximation of this system has a pair of imaginary eigenvalues. The non-linear part of this system can be represented as the sum of the forms of the component of a phase vector. Number k is the order of the forms more, than 2. Number k is natural even number. The algorithm for the proof of existence center in a neighbourhood of zero solution has been received.



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