Open AccessOn the kolmogorov system with fourth-degree homogeneous nonlinearities
Author(s) -
А. П. Садовский
Publication year - 2020
Publication title -
doklady nacionalʹnoj akademii nauk belarusi
Language(s) - English
Resource type - Journals
eISSN - 2524-2431
pISSN - 1561-8323
DOI - 10.29235/1561-8323-2020-64-3-268-272
Subject(s) - center (category theory) , homogeneous , degree (music) , mathematics , work (physics) , point (geometry) , singular point of a curve , mathematical analysis , calculus (dental) , combinatorics , physics , geometry , thermodynamics , medicine , chemistry , dentistry , acoustics , crystallography
The necessary conditions of the center at the singular point O (0, 0) for the kolmogorov system with fourth-degree homogeneous nonlinearities are found in the work of B. Ferenc, J. Dzheny, W. Liu, V. G. Romanovsky. For all these cases, with the exception of two, sufficiency is also proved. In the present article, sufficiency is proved for two cases of the center that were not proved in the above-mentioned work. In addition, the sufficiency of two other conditions of the center is proved in another way.