{"title":"用第一近似法研究微分系统的完全振荡、旋转和徘徊特性","authors":"I. N. Sergeev","doi":"10.1134/s0001434624030313","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The concepts of complete oscillation, rotation, and wandering as well as complete nonoscillation, nonrotation, and nonwandering of a system of differential equations (with respect to its zero solution) are introduced. A one-to-one relationship between these properties and the corresponding characteristics of the system is established. Signs of a guaranteed possibility of studying them using the first approximation system, as well as examples for which that is not possible, are given. </p>","PeriodicalId":18294,"journal":{"name":"Mathematical Notes","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation\",\"authors\":\"I. N. Sergeev\",\"doi\":\"10.1134/s0001434624030313\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p> The concepts of complete oscillation, rotation, and wandering as well as complete nonoscillation, nonrotation, and nonwandering of a system of differential equations (with respect to its zero solution) are introduced. A one-to-one relationship between these properties and the corresponding characteristics of the system is established. Signs of a guaranteed possibility of studying them using the first approximation system, as well as examples for which that is not possible, are given. </p>\",\"PeriodicalId\":18294,\"journal\":{\"name\":\"Mathematical Notes\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Notes\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0001434624030313\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Notes","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0001434624030313","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Study of the Complete Oscillation, Rotation, and Wandering Properties of a Differential System by the First Approximation
Abstract
The concepts of complete oscillation, rotation, and wandering as well as complete nonoscillation, nonrotation, and nonwandering of a system of differential equations (with respect to its zero solution) are introduced. A one-to-one relationship between these properties and the corresponding characteristics of the system is established. Signs of a guaranteed possibility of studying them using the first approximation system, as well as examples for which that is not possible, are given.
期刊介绍：
Mathematical Notes is a journal that publishes research papers and review articles in modern algebra, geometry and number theory, functional analysis, logic, set and measure theory, topology, probability and stochastics, differential and noncommutative geometry, operator and group theory, asymptotic and approximation methods, mathematical finance, linear and nonlinear equations, ergodic and spectral theory, operator algebras, and other related theoretical fields. It also presents rigorous results in mathematical physics.
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