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Reeb spaces of smooth functions on manifolds II 流形上光滑函数的里伯空间 II
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-03-14 DOI: 10.1007/s40687-024-00436-z
Osamu Saeki
{"title":"Reeb spaces of smooth functions on manifolds II","authors":"Osamu Saeki","doi":"10.1007/s40687-024-00436-z","DOIUrl":"https://doi.org/10.1007/s40687-024-00436-z","url":null,"abstract":"<p>The Reeb space of a continuous function on a topological space is the space of connected components of the level sets. In this paper we characterize those smooth functions on closed manifolds whose Reeb spaces have the structure of a finite graph. We also give several explicit examples of smooth functions on closed manifolds such that they themselves or their Reeb spaces have some interesting properties.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"55 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140146360","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Synchrony patterns in Laplacian networks 拉普拉斯网络中的同步模式
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-03-14 DOI: 10.1007/s40687-024-00428-z
{"title":"Synchrony patterns in Laplacian networks","authors":"","doi":"10.1007/s40687-024-00428-z","DOIUrl":"https://doi.org/10.1007/s40687-024-00428-z","url":null,"abstract":"<h3>Abstract</h3> <p>A network of coupled dynamical systems is represented by a graph whose vertices represent individual cells and whose edges represent couplings between cells. Motivated by the impact of synchronization results of the Kuramoto networks, we introduce the generalized class of Laplacian networks, governed by mappings whose Jacobian at any point is a symmetric matrix with row entries summing to zero. By recognizing this matrix with a weighted Laplacian of the associated graph, we derive the optimal estimates of its positive, null and negative eigenvalues directly from the graph topology. Furthermore, we provide a characterization of the mappings that define Laplacian networks. Lastly, we discuss stability of equilibria inside synchrony subspaces for two types of Laplacian network on a ring with some extra couplings.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"105 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140146361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On real algebraic links in the 3-sphere associated with mixed polynomials 论与混合多项式相关的 3 球中的实代数联系
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-03-08 DOI: 10.1007/s40687-024-00424-3
Raimundo N. Araújo dos Santos, Eder L. Sanchez Quiceno
{"title":"On real algebraic links in the 3-sphere associated with mixed polynomials","authors":"Raimundo N. Araújo dos Santos, Eder L. Sanchez Quiceno","doi":"10.1007/s40687-024-00424-3","DOIUrl":"https://doi.org/10.1007/s40687-024-00424-3","url":null,"abstract":"<p>In this paper we construct new classes of mixed singularities that provide realizations of real algebraic links in the 3-sphere. Especially, we describe this construction in the case of semiholomorphic polynomials, which are mixed polynomials that are holomorphic in one variable. Classifications and characterizations of real algebraic links are still open. These new classes of mixed singularities may help to shed light on the Benedetti–Shiota conjecture, which states that any fibered link on the 3-sphere is a real algebraic link.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"54 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140071617","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bi-Hölder equivalence of real analytic functions 实解析函数的双荷尔德等价性
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-03-07 DOI: 10.1007/s40687-024-00429-y
{"title":"Bi-Hölder equivalence of real analytic functions","authors":"","doi":"10.1007/s40687-024-00429-y","DOIUrl":"https://doi.org/10.1007/s40687-024-00429-y","url":null,"abstract":"<h3>Abstract</h3> <p>In this work, we show that Hölder equivalence of analytic functions germs <span> <span>(({mathbb {R}}^2,0)rightarrow ({mathbb {R}},0))</span> </span> admits continuous moduli.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"35 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140071814","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global planar dynamics with a star node and contracting nonlinearity 带有星形节点和收缩非线性的全局平面动力学
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-03-07 DOI: 10.1007/s40687-024-00427-0
Begoña Alarcón, Sofia B. S. D. Castro, Isabel S. Labouriau
{"title":"Global planar dynamics with a star node and contracting nonlinearity","authors":"Begoña Alarcón, Sofia B. S. D. Castro, Isabel S. Labouriau","doi":"10.1007/s40687-024-00427-0","DOIUrl":"https://doi.org/10.1007/s40687-024-00427-0","url":null,"abstract":"<p>This is a complete study of the dynamics of polynomial planar vector fields whose linear part is a multiple of the identity and whose nonlinear part is a contracting homogeneous polynomial. The contracting nonlinearity provides the existence of an invariant circle and allows us to obtain a classification through a complete invariant for the dynamics, extending previous work by other authors that was mainly concerned with the existence and number of limit cycles. The general results are also applied to some classes of examples: definite nonlinearities, <span>({textbf {Z}}_2oplus {textbf {Z}}_2)</span> symmetric systems and nonlinearities of degree 3, for which we provide complete sets of phase-portraits.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140071668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Milnor fibration theorem for differentiable maps 可变映射的米尔诺纤维定理
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-03-05 DOI: 10.1007/s40687-024-00431-4
José Luis Cisneros-Molina, Aurélio Menegon
{"title":"Milnor fibration theorem for differentiable maps","authors":"José Luis Cisneros-Molina, Aurélio Menegon","doi":"10.1007/s40687-024-00431-4","DOIUrl":"https://doi.org/10.1007/s40687-024-00431-4","url":null,"abstract":"<p>In Cisneros-Molina et al. (São Paulo J Math Sci, 2023. https://doi.org/10.1007/s40863-023-00370-y) it was proved the existence of fibrations à la Milnor (in the tube and in the sphere) for real analytic maps <span>(f:({mathbb {R}}^n,0) rightarrow ({mathbb {R}}^k,0))</span>, where <span>(nge kge 2)</span>, with non-isolated critical values. In the present article we extend the existence of the fibrations given in Cisneros-Molina et al. (São Paulo J Math Sci, 2023. https://doi.org/10.1007/s40863-023-00370-y) to differentiable maps of class <span>(C^{ell })</span>, <span>(ell ge 2)</span>, with possibly non-isolated critical value. This is done using a version of Ehresmann fibration theorem for differentiable maps of class <span>(C^{ell })</span> between smooth manifolds, which is a generalization of the proof given by Wolf (Michigan Math J 11:65–70, 1964) of Ehresmann fibration theorem. We also present a detailed example of a non-analytic map which has the aforementioned fibrations.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"38 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140045961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
De Rham-Witt KZ equations 德拉姆-维特 KZ方程
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-03-04 DOI: 10.1007/s40687-024-00425-2
{"title":"De Rham-Witt KZ equations","authors":"","doi":"10.1007/s40687-024-00425-2","DOIUrl":"https://doi.org/10.1007/s40687-024-00425-2","url":null,"abstract":"<h3>Abstract</h3> <p>In this paper we propose a de Rham-Witt version of the derived KZ equations and their hypergeometric realizations.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"10 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140033002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Duality and geometry of horocyclic evolutes in hyperbolic plane 双曲面中角环演化的对偶性和几何学
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-29 DOI: 10.1007/s40687-024-00434-1
Liang Chen, Shyuichi Izumiya, Masatomo Takahashi
{"title":"Duality and geometry of horocyclic evolutes in hyperbolic plane","authors":"Liang Chen, Shyuichi Izumiya, Masatomo Takahashi","doi":"10.1007/s40687-024-00434-1","DOIUrl":"https://doi.org/10.1007/s40687-024-00434-1","url":null,"abstract":"<p>We investigate geometric properties of a special kind of evolutes, so-called horocyclic evolutes, of smooth curves in hyperbolic plane from the viewpoint of duality. To do that, we first review the basic notions of (spacelike) frontals in hyperbolic plane, which developed by the first and the third authors by using basic Legendrian duality theorem developed by the second author. Moreover, two kinds of horocyclic evolutes are defined and the relationship between these two different evolutes are studied. As results, they are Legendrian dual to each other.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"50 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140011582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Image of iterated polynomial maps of the real plane 实平面多项式迭代映射的图像
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-28 DOI: 10.1007/s40687-024-00433-2
Tat Thang Nguyen
{"title":"Image of iterated polynomial maps of the real plane","authors":"Tat Thang Nguyen","doi":"10.1007/s40687-024-00433-2","DOIUrl":"https://doi.org/10.1007/s40687-024-00433-2","url":null,"abstract":"<p>Let <span>(F: {mathbb {R}}^2rightarrow {mathbb {R}}^2)</span> be a polynomial mapping. We consider the image of the compositions <span>(F^k)</span> of <i>F</i>. We prove that under some condition then the image of the iterated map <span>(F^k)</span> is stable when <i>k</i> is large.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"20 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Zariski invariant for quasi-ordinary hypersurfaces 准平凡超曲面的扎里斯基不变式
IF 1.2 3区 数学
Research in the Mathematical Sciences Pub Date : 2024-02-28 DOI: 10.1007/s40687-024-00430-5
R. A. Barbosa, M. E. Hernandes
{"title":"Zariski invariant for quasi-ordinary hypersurfaces","authors":"R. A. Barbosa, M. E. Hernandes","doi":"10.1007/s40687-024-00430-5","DOIUrl":"https://doi.org/10.1007/s40687-024-00430-5","url":null,"abstract":"<p>We introduced an <span>(tilde{mathcal {A}})</span>-invariant for quasi-ordinary parameterizations, and we consider it to describe quasi-ordinary surfaces with one generalized characteristic exponent admitting a countable moduli.</p>","PeriodicalId":48561,"journal":{"name":"Research in the Mathematical Sciences","volume":"18 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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