{"title":"一种真正的腐蚀性类型","authors":"V. Sedykh","doi":"10.1070/IM9015","DOIUrl":null,"url":null,"abstract":"We prove that the manifold of non-singular points of a stable real caustic germ of type and the manifolds of points of transversal intersection of its smooth branches consist only of contractible connected components. We also calculate the number of these components.","PeriodicalId":54910,"journal":{"name":"Izvestiya Mathematics","volume":"24 1","pages":"279 - 305"},"PeriodicalIF":0.8000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On a real caustic of type\",\"authors\":\"V. Sedykh\",\"doi\":\"10.1070/IM9015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that the manifold of non-singular points of a stable real caustic germ of type and the manifolds of points of transversal intersection of its smooth branches consist only of contractible connected components. We also calculate the number of these components.\",\"PeriodicalId\":54910,\"journal\":{\"name\":\"Izvestiya Mathematics\",\"volume\":\"24 1\",\"pages\":\"279 - 305\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1070/IM9015\",\"RegionNum\":3,\"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":"Izvestiya Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1070/IM9015","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We prove that the manifold of non-singular points of a stable real caustic germ of type and the manifolds of points of transversal intersection of its smooth branches consist only of contractible connected components. We also calculate the number of these components.
期刊介绍:
The Russian original is rigorously refereed in Russia and the translations are carefully scrutinised and edited by the London Mathematical Society. This publication covers all fields of mathematics, but special attention is given to:
Algebra;
Mathematical logic;
Number theory;
Mathematical analysis;
Geometry;
Topology;
Differential equations.