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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
{"title":"n-Generalized Schützenberger-Crossed Product of Monoids","authors":"Esra Kırmızı Çetinalp","doi":"10.1007/s11253-024-02321-y","DOIUrl":"https://doi.org/10.1007/s11253-024-02321-y","url":null,"abstract":"<p>We study the <i>n</i>-generalized Schützenberger-crossed product from the viewpoint of combinatorial group theory and introduce a new version of this product. For given monoids of this new product, we obtain a representation of the <i>n</i>-generalized Schützenberger-crossed product of arbitrary monoids. In addition, we give necessary and sufficient conditions for the regularity of this product.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142211195","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
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":"<p>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.</p><p>Ya. G. Sinai was the first who constructed and used Markov partitions for Anosov’s diffeomorphisms [<i>Funk. Anal. Prilozh.</i>, <b>2</b>, No 1, 64; No 3, 70 (1968); <b><i>English translation:</i></b> <i>Funct. Anal. Appl.</i>, <b>2</b>, No 1, 61; No 3, 245 (1968)]. Expanding endomorphisms regarded as the simplest representatives of endomorphisms were first studied by M. Shub [<i>Amer. J. Math.</i>, <b>91</b>, No 1, 175 (1969)]. To construct Markov partitions for expanding endomorphisms, we update Sinai’s approach in the proper way.</p><p>A more detailed historical overview can be found in the work by O. M. Sharkovsky [<i>Ukr. Mat. Zh.</i>, <b>74</b>, No. 12, 1709 (2023); <b><i>English translation:</i></b> <i>Ukr. Math. J.</i>, <b>74</b>, No. 12, 1950 (2023)]. In this work, Sharkovsky indicated that the methods used to prove the main results presented in [<i>Dokl. Akad. Nauk SSSR</i>, <b>170</b>, No. 6, 1276 (1966); <b><i>English translation:</i></b> <i>Sov. Math. Dokl.</i>, <b>7</b>, 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.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"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
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
{"title":"A Fitted Approximate Method for Solving Singularly Perturbed Volterra–Fredholm Integrodifferential Equations with Integral Boundary Condition","authors":"Baransel Gunes, Musa Cakir","doi":"10.1007/s11253-024-02312-z","DOIUrl":"https://doi.org/10.1007/s11253-024-02312-z","url":null,"abstract":"<p>We consider a novel numerical approach for solving boundary-value problems for the second-order Volterra-Fredholm integrodifferential equation with layer behavior and an integral boundary condition. A finite-difference scheme is proposed on suitable Shishkin-type mesh to obtain an approximate solution of the presented problem. It is proved that the method is first-order convergent in the discrete maximum norm. Two numerical examples are included to show the efficiency of the method.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871799","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
{"title":"SRB Measures for Some Stretched Hénon-Like Maps","authors":"Michael Jakobson, Sheldon Newhouse","doi":"10.1007/s11253-024-02310-1","DOIUrl":"https://doi.org/10.1007/s11253-024-02310-1","url":null,"abstract":"<p>We discuss the construction of SRB measures for some families of stretched Hénon-like maps.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871796","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
Periods of Self-Maps on $${mathbb{S}}^{2}$$ Via their Homology $${mathbb{S}}^{2}$上自映射的周期及其同调
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02308-9
Jaume Llibre
{"title":"Periods of Self-Maps on $${mathbb{S}}^{2}$$ Via their Homology","authors":"Jaume Llibre","doi":"10.1007/s11253-024-02308-9","DOIUrl":"https://doi.org/10.1007/s11253-024-02308-9","url":null,"abstract":"<p>As usual, we denote a 2-dimensional sphere by <span>({mathbb{S}}^{2})</span><i>.</i> We study the periods of periodic orbits of the maps <i>f</i> : <span>({mathbb{S}}^{2}to {mathbb{S}}^{2})</span> that are either continuous or <i>C</i><sup>1</sup> with all their periodic orbits being hyperbolic, or transversal, or holomorphic, or transversal holomorphic. For the first time, we summarize all known results on the periodic orbits of these distinct kinds of self-maps on <span>({mathbb{S}}^{2})</span> together. We note that every time when a map <i>f</i> : <span>({mathbb{S}}^{2}to {mathbb{S}}^{2})</span> increases its structure, the number of periodic orbits provided by its action on the homology increases.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871802","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
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
{"title":"Topological Entropy, Sets of Periods, and Transitivity for Circle Maps","authors":"Lluís Alsedà, Liane Bordignon, Jorge Groisman","doi":"10.1007/s11253-024-02305-y","DOIUrl":"https://doi.org/10.1007/s11253-024-02305-y","url":null,"abstract":"<p>Transitivity, the existence of periodic points, and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that, for every graph that is not a tree and any <i>ε</i> &gt; 0, there exist (complicated) totally transitive maps (then with cofinite set of periods) such that the topological entropy is smaller than <i>ε</i> (simplicity). To numerically measure the complexity of the set of periods, we introduce a notion of the <i>boundary of cofiniteness</i>. Larger boundary of cofiniteness corresponds to a simpler set of periods. We show that, for any continuous circle maps of degree one, every totally transitive (and, hence, robustly complicated) map with small topological entropy has arbitrarily large (simplicity) boundary of cofiniteness.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871798","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
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":"<p>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 <i>L</i>2-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.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"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
{"title":"Evolution of the Sharkovsky Theorem","authors":"Alexander Blokh, Michał Misiurewicz","doi":"10.1007/s11253-024-02306-x","DOIUrl":"https://doi.org/10.1007/s11253-024-02306-x","url":null,"abstract":"<p>We briefly describe some results that evolved from the Sharkovsky theorem.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871797","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
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
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02314-x
Xueyang Liu, Qi Wang
{"title":"Numerical Bifurcation of a Delayed Diffusive Hematopoiesis Model with Dirichlet Boundary Conditions","authors":"Xueyang Liu, Qi Wang","doi":"10.1007/s11253-024-02314-x","DOIUrl":"https://doi.org/10.1007/s11253-024-02314-x","url":null,"abstract":"<p>Numerical bifurcation of a delayed diffusive hematopoiesis model with Dirichlet boundary condition is studied by using a nonstandard finite-difference scheme. We prove that a series of numerical Neimark– Sacker bifurcations appears at the positive equilibrium as the time delay increases. At the same time, the parameter conditions for the existence of numerical Neimark–Sacker bifurcations at the point of positive equilibrium are presented. Finally, we present several examples to verify the accuracy of the accumulated results.</p>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873211","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
Coexistence of Cycles of a Continuous Map of the Real Line Into Itself 实线连续映射自身的循环共存
IF 0.5 4区 数学
Ukrainian Mathematical Journal Pub Date : 2024-07-30 DOI: 10.1007/s11253-024-02303-0
Oleksandr Sharkovsky
{"title":"Coexistence of Cycles of a Continuous Map of the Real Line Into Itself","authors":"Oleksandr Sharkovsky","doi":"10.1007/s11253-024-02303-0","DOIUrl":"https://doi.org/10.1007/s11253-024-02303-0","url":null,"abstract":"<p>Our main result can be formulated as follows: Consider the set of natural numbers in which the following relation is introduced: <i>n</i><sub>1</sub> precedes <i>n</i><sub>2</sub> (<i>n</i><sub>1</sub> ⪯ <i>n</i><sub>2</sub>) if, for any continuous map of the real line into itself, the existence of a cycle of order <i>n</i><sub>2</sub> follows from the existence of a cycle of order <i>n</i><sub>1</sub>. The following theorem is true:</p><p><b>Theorem.</b> <i>The introduced relation turns the set of natural numbers into an ordered set with the following ordering:</i>\u0000</p><span>$$3prec 5prec 7prec 9prec 11prec dots prec 3bullet 2prec 5bullet 2prec dots prec 3bullet {2}^{2}prec 5bullet {2}^{2}prec dots prec {2}^{3}prec {2}^{2}prec 2prec 1.$$</span>","PeriodicalId":49406,"journal":{"name":"Ukrainian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873212","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
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