{"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":50580,"journal":{"name":"Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":0.8000,"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\":50580,\"journal\":{\"name\":\"Differential Equations\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0012266124010026\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0012266124010026","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.
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