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О периодических сдвигах на n-мерном торе
Динамические системы. 2017. Т. 7. № 2. С. 113-118.
Kurenkov E., Рязанова К. А.
Keywords: топологическая сопряженностьtopological conjugacyгомотопияtoral automorphismshomotopyавтоморфизмы тора
Publication based on the results of:
Kurenkov E., Динамические системы 2015 Т. 5 № 1-2 С. 57-60
In this paper we consider endomorphisms given on 2-manifold satisfying axiom A. F. Przytycki obtained necessary and sufficient conditions for $\Omega$-stability of such endomorphisms. He also showed that in every neighborhood of an omega-unstable endomorphism a countable number of pairwise omega non-conjugate endomorphisms exists. Here we introduce an example of one-parametric family of endomorphisms of ...
Added: January 26, 2016
Gurevich E., Макаров А. А., Труды Средневолжского математического общества 2020 Т. 22 № 3 С. 261-267
We consider a class $H(\mathbb{R}^n)$ of orientation preserving homeomorphisms of Euclidean space $\mathbb{R}^n$ such that for any homeomorphism $h\in H(\mathbb{R}^n)$ and for any point $x\in \mathbb{R}^n$ a condition $\lim \limits_{n\to +\infty}h^n(x)\to O$ holds, were $O$ is the origin. It is provided that for any $n\geq 1$ an arbitrary homeomorphism $h\in H(\mathbb{R}^n)$ is topologically conjugated with ...
Added: September 14, 2020
Митрякова Т. М., Pochinka O., Журнал Средневолжского математического общества 2014 Т. 16 № 2 С. 76-79
In present paper we consider a class of 3-manifolds' diffeomorphisms lying on the border of a set of gradient-like systems and different from the last not more than one tangencies' orbits of two-dimensional separatrices. It is proved that for studying diffeomorphisms necessary and sufficient condition for topological conjugacy of two diffeomorphisms from this class is ...
Added: August 9, 2014
Golikova L., Pochinka O., Огарёв-Online 2020 № 13 С. 1-11
The first section of this article presents the basic definitions of the topic, the second chapter focuses on structurally stable circle transformations, and the last chapter is dedicated to suspensions on model transformation of S1. The basic results of the research are theorem 3.1 about equivalence of suspensions on model diffeomorphisms and statement 4.1 that ...
Added: November 23, 2020
Gurevich E., Смирнова А. С., Динамические системы 2018 Т. 2 № 15 С. 159-172
We consider a class $G$ of Morse-Smale diffeomorphisms on the sphere $S^n$ of dimension $n\geq 4$ such that invariant manifolds of different saddle periodic points of any diffeomorphisms from $G$ have no intersection. Dynamics of an arbitrary diffeomorphism $f\in G$ can be represented as ``sink-source'' dynamics where the ``sink'' $A_f$ (the ``source'' $R_f$) is the ...
Added: November 2, 2018
Grines E. A., Pochinka O., Динамические системы 2013 Vol. 3 No. 31 P. 185-200
In present paper we consider a class of 3-dimensional diffeomorphisms with finite hyperbolic chain recurrent set and finite number of orbits of heteroclinic tangencies. We prove that necessary conditions for topological conjugacy of two diffeomorphisms from this class is a generalization of moduli of stability for analogous two-dimensional systems.} ...
Added: August 10, 2014
Pochinka O., Левченко Ю. А., Grines V., Нелинейная динамика 2014 Т. 10 № 1 С. 17-33
Consider the class of diffeomorphisms of three-dimensional manifolds and satisfying aksiomA by Smale on the assumption that the non-wandering set of each diffeomorphism consists of surface two-dimensional basic sets. We find interrelations between the dynamics of such a diffeomorphism and the topology of the ambient manifold. Also found that each such diffeomorphism is Ω-conjugate to ...
Added: August 16, 2014
О. В. Починка, Е. А. Таланова, Д. Д. Шубин, Математический сборник 2023 Т. 214 № 8 С. 94-107
It is known that the topological conjugacy of gradient-like 3-difepheromorphisms with a single saddle point is completely determined by the equivalence of Hopf knots on the manifold of S^2 × S^1, which are the projections of a one-dimensional saddle separatics in the basin of node point, and the ambient manifold for all such diffeomorphisms is ...
Added: July 27, 2023
Kochetkov Y., Фундаментальная и прикладная математика 2013 Т. 18 № 6 С. 161-170
Многочлен, у которого ровно два критических значения, называется обобщенным многочленом Чебышева (или многочленом Шабата). Многочлен, у которого ровно три критических значения, называется многочленом Золотарева. Два многочлена Чебышева $f$ и $g$ называются Z-гомотопными, если существует семейство многочленов $p_a$, $a\in [0,1]$, где $p_0=f$, $p_1=g$ и $p_a$, $a\in (0,1)$, -- многочлен Золотарева. Так как многочлен Чебышева задает плоское ...
Added: September 11, 2014
Nozdrinov A., Починка А. И., Журнал Средневолжского математического общества 2023 Т. 25 № 1 С. 531-541
In this paper we consider gradient-like Morse-Smale diffeomorphisms defined on the three-dimensional sphere S 3 . For such diffeomorphisms, a complete invariant of topological conjugacy was obtained in the works of C. Bonatti, V. Grines, V. Medvedev, E. Pecu. It is an equivalence class of a set of homotopically non-trivially embedded tori and Klein bottles ...
Added: March 22, 2023
Safonov K., Малкин М. И., Journal of Physics: Conference Series 2018 Vol. 990 P. 012007
For onedimensional piecewise monotone discontionuous maps without periodic points, the 1-conformal measures are constructed and, as a corollary, semiconjugacy to piecewise linear models of constant (in absolute value) slope is obtained. It turns out that for generalized interval exchange transformations, the constructed semiconjugacy is, in fact, conjugacy . ...
Added: October 31, 2020
Kruglov V., Malyshev D., Pochinka O. et al., Discrete and Continuous Dynamical Systems 2020
In this paper, we study gradient-like flows without heteroclinic intersections on n-sphere up to topological conjugacy. We prove that such a flow is completely defined by a bi-colour tree corresponding to a skeleton formed by co-dimension one separatrices. Moreover, we show that such a tree is a complete invariant for these flows with respect to ...
Added: October 17, 2019
Zhdanovskiy I., Communications in Algebra 2021 Vol. 49 No. 1 P. 43-57
In this article, we study homotopes of finite-dimensional algebras (not necessarily, associative). In the case of associative algebras, we study homotopes by the methods of Category theory and give description of the so-called well-tempered elements of finite-dimensional associative algebra in algebraic terms. ...
Added: September 3, 2021
Pochinka O., Митрякова Т. М., Математические заметки 2013 Т. 93 № 6 С. 902-919
В настоящей статье разработан метод построения каскадов на поверхностях, позволяющих моделировать негрубые дискретные динамические системы с конечным числом орбит гетероклинического касания и заданными модулями топологической сопряженности ...
Added: March 25, 2014
Kruglov V., Malyshev D., Pochinka O. et al., Regular and Chaotic Dynamics 2020 Vol. 25 No. 6 P. 716-728
In this paper, we study gradient-like flows without heteroclinic intersections on n-sphere up to topological conjugacy. We prove that such a flow is completely defined by a bi-colour tree corresponding to a skeleton formed by co-dimension one separatrices. Moreover, we show that such a tree is a complete invariant for these
flows with respect to the ...
Added: November 15, 2020
Kruglov V., Pochinka O., Journal of Mathematical Sciences 2020 Vol. 250 P. 22-30
We study gradient-like flows with no heteroclinic intersections on an n-dimensional (n ≥ 3) sphere from the point of view of topological conjugacy. We prove that the topological conjugacy class of such a flow is completely determined by the bicolor tree corresponding to the frame of separatrices of codimension 1. We show that for such ...
Added: October 8, 2020
Kruglov V., Журнал Средневолжского математического общества 2018 Т. 20 № 4 С. 419-428
In 1978 J. Palis invented continuum topologically non-conjugate systems in a neighbourhood of a system with a heteroclinic contact (moduli). W. de Melo and С. van Strien in 1987 described a diffeomorphism class with a finite number of moduli: a chain of saddles taking part in the heteroclinic contact of such diffeomorphism includes not more ...
Added: November 21, 2018
Grines V., Pochinka O., Шиловская А. А., Труды Средневолжского математического общества 2016 Т. 18 № 1 С. 17-26
In this paper we consider the class G of A-dieomorphisms f , dened on a closed 3-manifold M3 . The nonwandering set is located on nite number of pairwise disjoint f -invariant 2-tori embedded in M3 . Each torus T is a union of $W^u_{B_T}\cup W^u_{\Sigma_T}$, либо $W^s_{B_T}\cup W^s_{\Sigma_T}$, where $B_T$ -- dimensional basic set exteriorly situated on T and T ...
Added: June 8, 2016
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017