{"title":"三维尼延胡斯算子的初等微分奇异性","authors":"D. Akpan, A. Oshemkov","doi":"10.1134/S1061920823040015","DOIUrl":null,"url":null,"abstract":"<p> In the paper, three-dimensional Nijenhuis operators are studied that have differential singularities, i.e., such points at which the coefficients of the characteristic polynomials are dependent. The case is studied in which the differentials of all invariants of the Nijenhuis operator are proportional, as well as the case when two invariants are functionally independent and the third defines a fold-type singularity. In particular, new examples of three-dimensional Nijenhuis operators with singularities of the specified type are constructed. </p><p> <b> DOI</b> 10.1134/S1061920823040015 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"425 - 431"},"PeriodicalIF":1.7000,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Elementary Differential Singularities of Three-Dimensional Nijenhuis Operators\",\"authors\":\"D. Akpan, A. Oshemkov\",\"doi\":\"10.1134/S1061920823040015\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> In the paper, three-dimensional Nijenhuis operators are studied that have differential singularities, i.e., such points at which the coefficients of the characteristic polynomials are dependent. The case is studied in which the differentials of all invariants of the Nijenhuis operator are proportional, as well as the case when two invariants are functionally independent and the third defines a fold-type singularity. In particular, new examples of three-dimensional Nijenhuis operators with singularities of the specified type are constructed. </p><p> <b> DOI</b> 10.1134/S1061920823040015 </p>\",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"30 4\",\"pages\":\"425 - 431\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2023-12-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Russian Journal of Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1134/S1061920823040015\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823040015","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
摘要
摘要 本文研究了具有微分奇点的三维尼延胡斯算子，即特征多项式系数相关的点。本文研究了尼延胡斯算子所有不变式的微分都成比例的情况，以及两个不变式在函数上是独立的，而第三个不变式定义了折叠型奇点的情况。特别是，我们构建了具有指定类型奇点的三维尼延胡斯算子的新实例。 doi 10.1134/s1061920823040015
Elementary Differential Singularities of Three-Dimensional Nijenhuis Operators
In the paper, three-dimensional Nijenhuis operators are studied that have differential singularities, i.e., such points at which the coefficients of the characteristic polynomials are dependent. The case is studied in which the differentials of all invariants of the Nijenhuis operator are proportional, as well as the case when two invariants are functionally independent and the third defines a fold-type singularity. In particular, new examples of three-dimensional Nijenhuis operators with singularities of the specified type are constructed.
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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