{"title":"动力学系统定性理论中的伪延拓","authors":"B. Kalitine","doi":"10.33581/2520-6508-2022-3-45-53","DOIUrl":null,"url":null,"abstract":"This paper considers the qualitative behaviour of the flow in a neighbourhood of closed invariant sets of dynamical systems. The properties of compactness, invariance, and connectivity of pseudo-prolongations are investigated. A rather deep analysis of the flow in the vicinity of a compact invariant set of asymptotically compact phase spaces is presented. The connection of pseudo-prolongation with the first positive prolongation of T. Ura and the set of weakly elliptic points is refined.","PeriodicalId":36323,"journal":{"name":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pseudo-prolongations in the qualitative theory of dynamical systems\",\"authors\":\"B. Kalitine\",\"doi\":\"10.33581/2520-6508-2022-3-45-53\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper considers the qualitative behaviour of the flow in a neighbourhood of closed invariant sets of dynamical systems. The properties of compactness, invariance, and connectivity of pseudo-prolongations are investigated. A rather deep analysis of the flow in the vicinity of a compact invariant set of asymptotically compact phase spaces is presented. The connection of pseudo-prolongation with the first positive prolongation of T. Ura and the set of weakly elliptic points is refined.\",\"PeriodicalId\":36323,\"journal\":{\"name\":\"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33581/2520-6508-2022-3-45-53\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zhurnal Belorusskogo Gosudarstvennogo Universiteta. Matematika. Informatika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33581/2520-6508-2022-3-45-53","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Pseudo-prolongations in the qualitative theory of dynamical systems
This paper considers the qualitative behaviour of the flow in a neighbourhood of closed invariant sets of dynamical systems. The properties of compactness, invariance, and connectivity of pseudo-prolongations are investigated. A rather deep analysis of the flow in the vicinity of a compact invariant set of asymptotically compact phase spaces is presented. The connection of pseudo-prolongation with the first positive prolongation of T. Ura and the set of weakly elliptic points is refined.
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