{"title":"接触单峰图病菌从一个平面到另一个平面","authors":"M. Binyamin, S. Aslam, Khawar Mehmood","doi":"10.5802/crmath.114","DOIUrl":null,"url":null,"abstract":"In this article, we correct the classification of unimodal map germs from the plane to the plane of Boardman symbol (2,2) given by Dimca and Gibson. Also, we characterize this classification of unimodal map germs in terms of certain invariants. Moreover, on the basis of this characterization we present an algorithm to compute the type of unimodal map germs of the Boardman symbol (2,2) without computing the normal form and give its implementation in the computer algebra system Singular [8]. 2020 Mathematics Subject Classification. 58Q05, 14H20. Funding. The research of the first author is supported by Higher Education Commission, Pakistan by the Project Number 7495/Punjab/NRPU/R&D/HEC/2017. Manuscript received 21st July 2020, accepted 8th September 2020.","PeriodicalId":10620,"journal":{"name":"Comptes Rendus Mathematique","volume":"358 1","pages":"923-930"},"PeriodicalIF":0.8000,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Contact unimodal map germs from the plane to the plane\",\"authors\":\"M. Binyamin, S. Aslam, Khawar Mehmood\",\"doi\":\"10.5802/crmath.114\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, we correct the classification of unimodal map germs from the plane to the plane of Boardman symbol (2,2) given by Dimca and Gibson. Also, we characterize this classification of unimodal map germs in terms of certain invariants. Moreover, on the basis of this characterization we present an algorithm to compute the type of unimodal map germs of the Boardman symbol (2,2) without computing the normal form and give its implementation in the computer algebra system Singular [8]. 2020 Mathematics Subject Classification. 58Q05, 14H20. Funding. The research of the first author is supported by Higher Education Commission, Pakistan by the Project Number 7495/Punjab/NRPU/R&D/HEC/2017. Manuscript received 21st July 2020, accepted 8th September 2020.\",\"PeriodicalId\":10620,\"journal\":{\"name\":\"Comptes Rendus Mathematique\",\"volume\":\"358 1\",\"pages\":\"923-930\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2020-12-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Comptes Rendus Mathematique\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/crmath.114\",\"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":"Comptes Rendus Mathematique","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/crmath.114","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Contact unimodal map germs from the plane to the plane
In this article, we correct the classification of unimodal map germs from the plane to the plane of Boardman symbol (2,2) given by Dimca and Gibson. Also, we characterize this classification of unimodal map germs in terms of certain invariants. Moreover, on the basis of this characterization we present an algorithm to compute the type of unimodal map germs of the Boardman symbol (2,2) without computing the normal form and give its implementation in the computer algebra system Singular [8]. 2020 Mathematics Subject Classification. 58Q05, 14H20. Funding. The research of the first author is supported by Higher Education Commission, Pakistan by the Project Number 7495/Punjab/NRPU/R&D/HEC/2017. Manuscript received 21st July 2020, accepted 8th September 2020.
期刊介绍:
The Comptes Rendus - Mathématique cover all fields of the discipline: Logic, Combinatorics, Number Theory, Group Theory, Mathematical Analysis, (Partial) Differential Equations, Geometry, Topology, Dynamical systems, Mathematical Physics, Mathematical Problems in Mechanics, Signal Theory, Mathematical Economics, …
Articles are original notes that briefly describe an important discovery or result. The articles are written in French or English.
The journal also publishes review papers, thematic issues and texts reflecting the activity of Académie des sciences in the field of Mathematics.