Ukrainian Mathematical Journal最新文献_第3页

n-Generalized Schützenberger-Crossed Product of Monoids n 广义胥岑伯格单体交叉积

IF 0.5 4区数学

Ukrainian Mathematical Journal Pub Date : 2024-08-15 DOI: 10.1007/s11253-024-02321-y

Esra Kırmızı Çetinalp

引用次数: 0

Locally Maximal Attractors of Expanding Dynamical Systems 扩展动力系统的局部最大吸引子

IF 0.5 4区数学

Ukrainian Mathematical Journal Pub Date : 2024-07-31 DOI: 10.1007/s11253-024-02304-z

Oleksandr Sharkovsky, Vasyl Bondarchuk, Andrii Sivak

{"title":"Locally Maximal Attractors of Expanding Dynamical Systems","authors":"Oleksandr Sharkovsky, Vasyl Bondarchuk, Andrii Sivak","doi":"10.1007/s11253-024-02304-z","DOIUrl":"https://doi.org/10.1007/s11253-024-02304-z","url":null,"abstract":"We study locally maximal attractors of expanding dynamical systems. Our main result is a representation of these attractors with the help of topological Markov chains corresponding to the Markov partitions of these attractors, which allows us to describe the dynamics of system on them.Ya. G. Sinai was the first who constructed and used Markov partitions for Anosov’s diffeomorphisms [Funk. Anal. Prilozh., 2, No 1, 64; No 3, 70 (1968); English translation: Funct. Anal. Appl., 2, No 1, 61; No 3, 245 (1968)]. Expanding endomorphisms regarded as the simplest representatives of endomorphisms were first studied by M. Shub [Amer. J. Math., 91, No 1, 175 (1969)]. To construct Markov partitions for expanding endomorphisms, we update Sinai’s approach in the proper way.A more detailed historical overview can be found in the work by O. M. Sharkovsky [Ukr. Mat. Zh., 74, No. 12, 1709 (2023); English translation: Ukr. Math. J., 74, No. 12, 1950 (2023)]. In this work, Sharkovsky indicated that the methods used to prove the main results presented in [Dokl. Akad. Nauk SSSR, 170, No. 6, 1276 (1966); English translation: Sov. Math. Dokl., 7, No. 5, 1384 (1966)] were, in fact, published in the collection of papers “Dynamical systems and the problems of stability of solutions of differential equations” (1973) issued by the Institute of Mathematics of the Academy of Sciences of Ukraine. This collection is difficultly accessible and was never translated into English. Note that, in the indicated paper, these methods were applied to somewhat different objects. To the best of our knowledge, there is no information about publications of similar results. In view of the outlined history and importance of the described approach (based on Markov partitions and topological Markov chains) for the description of construction of the attractors, it seems reasonable to publish these results anew.","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"20 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

SRB Measures for Some Stretched Hénon-Like Maps 一些拉伸的类似赫农地图的 SRB 度量

IF 0.5 4区数学

Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02310-1

Michael Jakobson, Sheldon Newhouse

引用次数: 0

Topological Entropy, Sets of Periods, and Transitivity for Circle Maps 圆图的拓扑熵、周期集和遍历性

IF 0.5 4区数学

Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02305-y

Lluís Alsedà, Liane Bordignon, Jorge Groisman

引用次数: 0

A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition 求解带积分边界条件的奇异扰动 Volterra-Fredholm 积分微分方程的拟合近似法

IF 0.5 4区数学

Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02312-z

Baransel Gunes, Musa Cakir

引用次数: 0

Periods of Self-Maps on $${mathbb{S}}^{2}$$ Via their Homology $${mathbb{S}}^{2}$上自映射的周期及其同调

IF 0.5 4区数学

Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02308-9

Jaume Llibre

引用次数: 0

On the Nonstandard Maximum Principle and Its Application for Construction of Monotone Finite-Difference Schemes for Multidimensional Quasilinear Parabolic Equations 论非标准最大值原理及其在构建多维准抛物方程单调有限差分方案中的应用

IF 0.5 4区数学

Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02313-y

Le Minh Hieu, Nguyen Huu Nguyen Xuan, Dang Ngoc Hoang Thanh

{"title":"On the Nonstandard Maximum Principle and Its Application for Construction of Monotone Finite-Difference Schemes for Multidimensional Quasilinear Parabolic Equations","authors":"Le Minh Hieu, Nguyen Huu Nguyen Xuan, Dang Ngoc Hoang Thanh","doi":"10.1007/s11253-024-02313-y","DOIUrl":"https://doi.org/10.1007/s11253-024-02313-y","url":null,"abstract":"We consider the difference maximum principle with input data of variable sign and its application to the investigation of the monotonicity and convergence of finite-difference schemes (FDSs). Namely, we consider the Dirichlet initial-boundary-value problem for multidimensional quasilinear parabolic equations with unbounded nonlinearity. Unconditionally monotone linearized finite-difference schemes of the second-order of accuracy are constructed on uniform grids. A two-sided estimate for the grid solution, which is completely consistent with similar estimates for the exact solution, is obtained. These estimates are used to prove the convergence of FDSs in the grid L2-norm. We also present a study aimed at constructing second-order monotone difference schemes for the parabolic convection-diffusion equation with boundary conditions of the third kind and unlimited nonlinearity without using the initial differential equation on the domain boundaries. The goal is a combination of the assumption of existence and uniqueness of a smooth solution and the regularization principle. In this case, the boundary conditions are directly approximated on a two-point stencil of the second order.","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":"194 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871795","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Evolution of the Sharkovsky Theorem 沙可夫斯基定理的演变

IF 0.5 4区数学

Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02306-x

Alexander Blokh, Michał Misiurewicz

引用次数: 0

On a Functional Equation Characterizing Some Probability Distributions 论表征某些概率分布的函数方程

IF 0.5 4区数学

Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02311-0

Justyna Jarczyk, Witold Jarczyk

引用次数: 0

Numerical Bifurcation of a Delayed Diffusive Hematopoiesis Model with Dirichlet Boundary Conditions 带 Dirichlet 边界条件的延迟扩散造血模型的数值分叉