Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva最新文献_第4页

Spherical flow diagram with finite hyperbolic chain-recurrent set 有限双曲链循环集的球面流程图

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-06-30 DOI: 10.15507/2079-6900.24.202202.132-140

Vladislav D. Galki, O. Pochinka

引用次数: 1

Uniqueness of the solution of one class of Volterra-Stieltjes linear integral equations of the third kind 一类第三类Volterra-Stieltjes线性积分方程解的唯一性

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-03-31 DOI: 10.15507/2079-6900.24.202201.11-20

A. Asanov, K. Matanova, Eliza Absamat kyzy

引用次数: 0

On the Movement of Gyrostat under the Action of Potential and Gyroscopic Forces 势能和陀螺力作用下陀螺陀螺的运动

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-03-31 DOI: 10.15507/2079-6900.24.202201.66-75

A. Kosov, È. Semenov

引用次数: 0

Classification of suspensions over cartesian products of orientation-reversing diffeomorphisms of a circle 圆方向反转微分同态笛卡尔积上悬架的分类

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-03-31 DOI: 10.15507/2079-6900.24.202201.54-65

S. Zinina, Pavel I. Pochinka

{"title":"Classification of suspensions over cartesian products of orientation-reversing diffeomorphisms of a circle","authors":"S. Zinina, Pavel I. Pochinka","doi":"10.15507/2079-6900.24.202201.54-65","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202201.54-65","url":null,"abstract":"This paper introduces class G containing Cartesian products of orientation-changing rough transformations of the circle and studies their dynamics. As it is known from the paper of A. G. Maier non-wandering set of orientation-changing diffeomorphism of the circle consists of 2q periodic points, where q is some natural number. So Cartesian products of two such diffeomorphisms has 4q1q2 periodic points where q1 corresponds to the first transformation and q2 corresponds to the second one. The authors describe all possible types of the set of periodic points, which contains 2q1q2 saddle points, q1q2 sinks, and q1q2 sources; 4 points from mentioned 4q1q2 periodic ones are fixed, and the remaining 4q1q2−4 points have period 2. In the theory of smooth dynamical systems, a very useful result is that, given a diffeomorphism f of a manifold, one can construct a flow on a manifold with dimension one greater; this flow is called the suspension over f. The authors introduce the concept of suspension over diffeomorphisms of class G, describe all possible types of suspension orbits and the number of these orbits. Besides that, the authors prove a theorem on the topology of the manifold on which the suspension is given. Namely, the carrier manifold of the flows under consideration is homeomorphic to the closed 3-manifold T2×[0,1]/φ, where φ:T2→T2. The main result of the paper says that suspensions over diffeomorphisms of the class G are topologically equivalent if and only if corresponding diffeomorphisms are topologically conjugate. The idea of the proof is to show that the topological equivalence of the suspensions ϕt and ϕ′t implies the topological conjugacy of ϕ and ϕ′.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131657870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Topological conjugacy of non-singular flows with two limit cycles on S2×S1 S2×S1上两极限环非奇异流的拓扑共轭性

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-03-31 DOI: 10.15507/2079-6900.24.202201.40-53

A. L. Dobrolyubova, V. Kruglov

{"title":"Topological conjugacy of non-singular flows with two limit cycles on S2×S1","authors":"A. L. Dobrolyubova, V. Kruglov","doi":"10.15507/2079-6900.24.202201.40-53","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202201.40-53","url":null,"abstract":"In the paper, non-singular flows with two limit cycles on the manifold S2×S1 are considered. For such flows, a classification is obtained up to topological conjugacy, and it is shown that they have a functional modulus of stability. Since the functional modulus of stability takes on its own value for each fixed argument, the presence of such modulus implies the presence of an infinite number of numerical moduli of stability. To obtain this result, linearization is carried out in the neighbourhoods of two limit cycles using the construction from the work by M. Irwin. A result is obtained on the presence of a two-dimensional foliation in a neighborhood of the limit cycle; this foliation is invariant up to topological conjugacy. Existence of the functional modulus of stability follows from the presence of such foliations. Namely, when considering the intersection of two foliations and, accordingly, two linearizations acting in the basins of two limit cycles, the desired functional modulus is a map describing the relative position of the foliation layer in the neighborhood of the first limit cycle relative to the layer of the second limit cycle. The results are used from the work by Pochinka O. V. and Shubin D. D. on exactly two classes of topological equivalence of flows in the class under consideration and on description of their differences. The work includes figure which shows 2 classes of topological conjugacy of flows from the classes studied. Also there is a figure which shows the process of gluing R3 into a manifold with a stable limit cycle. Moreover, the construction of a solid torus is shown. The figures show consistent and inconsistent orientation of limit cycles, as well as invariant foliations. Also there is a figure which shows the functional modulus.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122283406","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Endomorphisms and anti-endomorphisms of some finite groupoids 有限群类群的自同态与反自同态

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-03-31 DOI: 10.15507/2079-6900.24.202201.76-95

A. Litavrin

{"title":"Endomorphisms and anti-endomorphisms of some finite groupoids","authors":"A. Litavrin","doi":"10.15507/2079-6900.24.202201.76-95","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202201.76-95","url":null,"abstract":"In this paper, we study anti-endomorphisms of some finite groupoids. Previously, special groupoids S(k,q) of order k(1+k) with a generating set of k elements were introduced. Previously, the element-by-element description of the monoid of all endomorphisms (in particular, automorphisms) of a given groupoid was studied. It was shown that every finite monoid is isomorphically embeddable in the monoid of all endomorphisms of a suitable groupoid S(k,q). In recent article, we give an element-by-element description for the set of all anti-endomorphisms of the groupoid S(k,q). We establish that, depending on the groupoid S(k,q), the set of all its anti-endomorphisms may be closed or not closed under the composition of mappings. For an element-by-element description of anti-endomorphisms, we study the action of an arbitrary anti-endomorphism on generating elements of a groupoid. With this approach, the anti-endomorphism will fall into one of three classes. Anti-endomorphisms from the two classes obtained will be endomorphisms of given groupoid. The remaining class of anti-endomorphisms, depending on the particular groupoid S(k,q), may either consist or not consist of endomorphisms. In this paper, we study endomorphisms of some finite groupoids G whose order satisfies some inequality. We construct some endomorphisms of such groupoids and show that every finite monoid is isomorphically embedded in the monoid of all endomorphisms of a suitable groupoid G. To prove this result, we essentially use a generalization of Cayley's theorem to the case of monoids (semigroups with identity).","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126349570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Dynamical properties of direct products of discrete dynamical systems 离散动力系统直接积的动力学性质

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-03-31 DOI: 10.15507/2079-6900.24.202201.21-30

M. Barinova, Evgenia K. Shustova

{"title":"Dynamical properties of direct products of discrete dynamical systems","authors":"M. Barinova, Evgenia K. Shustova","doi":"10.15507/2079-6900.24.202201.21-30","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202201.21-30","url":null,"abstract":"A natural way for creating new dynamical systems is to consider direct products of already known systems. The paper studies some dynamical properties of direct products of homeomorphisms and diffeomorphisms. In particular, authors prove that a chain-recurrent set of the direct product of homeomorphisms is a direct product of the chain-recurrent sets. Another result established in the paper is that the direct product of diffeomorphisms holds hyperbolic structure on the direct product of hyperbolic sets. It is known that if a diffeomorphism has a hyperbolic chain-recurrent set, then this mapping is Ω-stable. Therefore, it follows from the results of the paper that the direct product of Ω-stable diffeomorphisms is also Ω-stable. Another question which is raised in the article concerns the existence of an energy function for the direct product of diffeomorphisms which already have such functions (recall that energy function is a smooth Lyapunov function whose set of critical points coincides with the chain-recurrent set of the system). Authors show that in this case the function can be found as a weighted sum of energy functions of initial diffeomorphisms.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"397 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114376885","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

On a topological classification of multidimensional polar flows 多维极流的拓扑分类

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2022-03-31 DOI: 10.15507/2079-6900.24.202201.31-39

E. Gurevich, Natalya S. Denisova

{"title":"On a topological classification of multidimensional polar flows","authors":"E. Gurevich, Natalya S. Denisova","doi":"10.15507/2079-6900.24.202201.31-39","DOIUrl":"https://doi.org/10.15507/2079-6900.24.202201.31-39","url":null,"abstract":"The work solves the classification problem for structurally stable flows, which goes back to the classical works of Andronov, Pontryagin, Leontovich and Mayer. One of important examples of such flows is so-called Morse-Smale flow, whose non-wandering set consists of a finite number of fixed points and periodic trajectories. To date, there are exhaustive classification results for Morse-Smale flows given on manifolds whose dimension does not exceed three, and a very small number of results for higher dimensions. This is explained by increasing complexity of the topological problems that arise while describing the structure of the partition of a multidimensional phase space into trajectories. In this paper authors investigate the class G(Mn) of Morse-Smale flows on a closed connected orientable manifold Mn whose non-wandering set consists of exactly four points: a source, a sink, and two saddles. For the case when the dimension n of the supporting manifold is greater or equal than four, it is additionally assumed that one of the invariant manifolds for each saddle equilibrium state is one-dimensional. For flows from this class, authors describe the topology of the supporting manifold, estimate minimum number of heteroclinic curves, and obtain necessary and sufficient conditions of topological equivalence. Authors also describe an algorithm that constructs standard representative in each class of topological equivalence. One of the surprising results of this paper is that while for n=3 there is a countable set of manifolds that admit flows from class G(M3), there is only one supporting manifold (up to homeomorphism) for dimension n>3.","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-03-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127320622","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Optimal with respect to accuracy methods for evaluating hypersingular integrals 求超奇异积分的最优精度方法

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2021-12-30 DOI: 10.15507/2079-6900.23.202104.360-378

I. Boykov, A. Boykova

{"title":"Optimal with respect to accuracy methods for evaluating hypersingular integrals","authors":"I. Boykov, A. Boykova","doi":"10.15507/2079-6900.23.202104.360-378","DOIUrl":"https://doi.org/10.15507/2079-6900.23.202104.360-378","url":null,"abstract":"In this paper we constructed optimal with respect to order quadrature formulas for evaluating one- and multidimensional hypersingular integrals on classes of functions Ωur,γ(Ω,M), Ω¯ur,γ(Ω,M), Ω=[−1,1]l, l=1,2,…,M=Const, and γ is a real positive number. The functions that belong to classes Ωur,γ(Ω,M) and Ω¯ur,γ(Ω,M) have bounded derivatives up to the rth order in domain Ω and derivatives up to the sth order (s=r+⌈γ⌉) in domain Ω∖Γ, Γ=∂Ω. Moduli of derivatives of the vth order (r<v≤s) are power functions of d(x,Γ)−1(1+|lnd(x,Γ)|), where d(x,Γ) is a distance between point x and Γ. The interest in these classes of functions is due to the fact that solutions of singular and hypersingular integral equations are their members. Moreover various physical fields, in particular gravitational and electromagnetic fields belong to these classes as well. We give definitions of optimal with respect to accuracy methods for solving hypersingular integrals. We constructed optimal with respect to order of accuracy quadrature formulas for evaluating one- and multidimensional hypersingular integrals on classes of functions Ωur,γ(Ω,M) and Ω¯ur,γ(Ω,M).","PeriodicalId":273445,"journal":{"name":"Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114068342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Simulation of switchers for CNOT-gates based on optical waveguide interaction with coupled mode theory 基于光波导耦合模式理论的cno -栅极开关仿真

Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva Pub Date : 2021-12-30 DOI: 10.15507/2079-6900.23.202104.433-443

A. A. Lytaev, I. Popov

引用次数: 0