{"title":"反射函数与第一积分概念的广义化","authors":"V. I. Mironenko, V. V. Mironenko","doi":"10.1134/s0012266124010026","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The relationships between the notion of generalized integral and the notions of reflecting\nfunction and Poincaré map (period map) for periodic differential systems are traced.\nThe notion of generalized first integral is used to study questions of the existence and stability of\nperiodic solutions of periodic differential systems and analyze the center–focus problem.\n</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Reflecting Function and a Generalization of the Notion of First Integral\",\"authors\":\"V. I. Mironenko, V. V. Mironenko\",\"doi\":\"10.1134/s0012266124010026\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> The relationships between the notion of generalized integral and the notions of reflecting\\nfunction and Poincaré map (period map) for periodic differential systems are traced.\\nThe notion of generalized first integral is used to study questions of the existence and stability of\\nperiodic solutions of periodic differential systems and analyze the center–focus problem.\\n</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266124010026\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124010026","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Reflecting Function and a Generalization of the Notion of First Integral
Abstract
The relationships between the notion of generalized integral and the notions of reflecting
function and Poincaré map (period map) for periodic differential systems are traced.
The notion of generalized first integral is used to study questions of the existence and stability of
periodic solutions of periodic differential systems and analyze the center–focus problem.
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