{"title":"关于四次齐次非线性kolmogorov系统","authors":"A. P. Sadovskiĭ","doi":"10.29235/1561-8323-2020-64-3-268-272","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":11283,"journal":{"name":"Doklady of the National Academy of Sciences of Belarus","volume":"119 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the kolmogorov system with fourth-degree homogeneous nonlinearities\",\"authors\":\"A. P. Sadovskiĭ\",\"doi\":\"10.29235/1561-8323-2020-64-3-268-272\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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.\",\"PeriodicalId\":11283,\"journal\":{\"name\":\"Doklady of the National Academy of Sciences of Belarus\",\"volume\":\"119 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-07-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Doklady of the National Academy of Sciences of Belarus\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.29235/1561-8323-2020-64-3-268-272\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady of the National Academy of Sciences of Belarus","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.29235/1561-8323-2020-64-3-268-272","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
在B. Ferenc, J. Dzheny, W. Liu, V. G. Romanovsky的工作中，得到了四次齐次非线性kolmogorov系统在奇点O(0,0)处中心存在的必要条件。除两种情况外，所有这些情况也都证明了充分性。本文对上述工作中未证明的两种中心的充分性进行了证明。此外，用另一种方法证明了中心的另外两个条件的充分性。
On the kolmogorov system with fourth-degree homogeneous nonlinearities
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.
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