{"title":"论尼延胡斯算子某些奇点的线性化","authors":"A.Yu. Konyaev","doi":"10.1134/S106192084010084","DOIUrl":null,"url":null,"abstract":"<p> We consider a linearization problem for Nijenhuis operators in dimension two around a point of scalar type in analytic category. The problem was almost completely solved in [8]. One case, however, namely the case of left-symmetric algebra <span>\\(\\mathfrak b_{1, \\alpha}\\)</span>, proved to be difficult. Here we solve it and, thus, complete the solution of the linearization problem for Nijenhuis operators in dimension two. The problem turns out to be related to classical results on the linearization of vector fields and their monodromy mappings. </p><p> <b> DOI</b> 10.1134/S106192084010084 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"31 1","pages":"106 - 111"},"PeriodicalIF":1.7000,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the Linearization of Certain Singularities of Nijenhuis Operators\",\"authors\":\"A.Yu. Konyaev\",\"doi\":\"10.1134/S106192084010084\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p> We consider a linearization problem for Nijenhuis operators in dimension two around a point of scalar type in analytic category. The problem was almost completely solved in [8]. One case, however, namely the case of left-symmetric algebra <span>\\\\(\\\\mathfrak b_{1, \\\\alpha}\\\\)</span>, proved to be difficult. Here we solve it and, thus, complete the solution of the linearization problem for Nijenhuis operators in dimension two. The problem turns out to be related to classical results on the linearization of vector fields and their monodromy mappings. </p><p> <b> DOI</b> 10.1134/S106192084010084 </p>\",\"PeriodicalId\":763,\"journal\":{\"name\":\"Russian Journal of Mathematical Physics\",\"volume\":\"31 1\",\"pages\":\"106 - 111\"},\"PeriodicalIF\":1.7000,\"publicationDate\":\"2024-03-19\",\"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/S106192084010084\",\"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/S106192084010084","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 我们考虑在二维中围绕解析范畴中的标量型点的尼延胡斯算子的线性化问题。这个问题在[8]中几乎被完全解决了。然而，有一种情况，即左对称代数 \(\mathfrak b_{1, \alpha}\)的情况，被证明是困难的。在这里，我们解决了这个问题，从而完成了对二维尼延胡斯算子线性化问题的求解。这个问题与向量场线性化及其单色映射的经典结果有关。 doi 10.1134/s106192084010084
On the Linearization of Certain Singularities of Nijenhuis Operators
We consider a linearization problem for Nijenhuis operators in dimension two around a point of scalar type in analytic category. The problem was almost completely solved in [8]. One case, however, namely the case of left-symmetric algebra \(\mathfrak b_{1, \alpha}\), proved to be difficult. Here we solve it and, thus, complete the solution of the linearization problem for Nijenhuis operators in dimension two. The problem turns out to be related to classical results on the linearization of vector fields and their monodromy mappings.
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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