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Реализация оснащённого двудольного графа Омега-устойчивым потоком на поверхности
Гл. 59. С. 418–427.
Kruglov V., Pochinka O.
A lot of many sorts of graphs (directed, multicolored, bipartite, etc.) were
repeatedly used to describe and realize systems with regular dynamics on surfaces. For
example, Morse-Smale flows are completely described by a directed graph equipped
with a subgraph system. In addition, their dynamics can be described by three-color
graphs. Four-color graphs describe the dynamics of some non structurally unstable
vector fields, and a directed bipartite graph, equipped with additional information,
is a complete topological invariant for Ω-stable flows. In this paper, for each oriented
equipped bipartite graph, we construct a standard Ω-stable flow on a closed surface.
Publication based on the results of:
In book
Саранск: Средневолжское математическое общество (СВМО), 2017.
A. L. Dobrolyubova, V. E. Kruglov, O. V. Pochinka, Journal of Mathematical Sciences 2023 Vol. 269 No. 2 P. 165–172
The simplest nonsingular flows on closed orientable 3-manifolds are studied. We establish
that each class of topological equivalence of the simplest nonsingular flow on a
lens consists of an infinite set of topological conjugacy classes. We obtain necessary
and sufficient conditions for the topological conjugacy of the flows under consideration. ...
Added: February 18, 2023
Obukhov A., Рытикова Н. А., Исследователь/Researcher 2021 № 3-4 С. 197–217
The article presents the original contest called “V Fokuse Vnimania” (In the Focus of Attention), which is one of the organizational conditions for increasing the research culture of students and teachers of the “26 KADR” College. The key-feature of the contest is that the participants themselves decide what type of expertise they want to receive ...
Added: April 1, 2022
Obukhov A., Kosaretsky S., Можаева М. В. et al., Исследователь/Researcher 2021 № 1-2 С. 32–51
The article presents the theoretical foundations and examples of the use of project and research activity methods, media resources and e-learning technologies for the formation and development of environmental literacy and environmentally responsible behavior in additional education programs. A model of three levels of student involvement in activities for the development of environmental literacy is ...
Added: October 11, 2021
Kruglov V., Pochinka O., Известия высших учебных заведений. Прикладная нелинейная динамика 2021 Т. 29 № 6 С. 835–850
Purpose. The purpose of this study is to consider the class of Morse-Smale flows on surfaces, to
characterize its subclass consisting of flows with a finite number of moduli of stability, and to obtain a topological
classification of such flows up to topological conjugacy, that is, to find an invariant that shows that there exists
a homeomorphism that ...
Added: October 5, 2021
Obukhov A., В кн.: Топос. Типовая модель создания новых мест для детского дополнительного образования туристско-краеведческой направленности.: М.: ФГБОУ ДО ФЦДЮКиТ, 2020. С. 52–62.
«Точка варения» − центр дополнительного образо- вания, расположенный на территории парка «Усадьба Трубецких в Хамовниках». Москва фактически стала экспериментальной площадкой и воплощением наших задумок по реализации модели «Топос», концепции открытого образовательного развивающего пространства как места рождения замыслов, проектов, исследований, места, где можно найти единомышленников, собрать команду исследователей, найти наставника, научного руководителя, обсудить текущие задачи, проблемы, ...
Added: November 30, 2020
Kolobianina A., Kruglov V., Журнал Средневолжского математического общества 2020 Т. 22 № 4 С. 434–441
In this paper, we consider the class of Ω-stable flows on surfaces, i.e. flows on surfaces with the non-wandering set consisting of a finite number of hyperbolic fixed points and a finite number of hyperbolic limit cycles. The class of Ω-stable flows is a generalization of the class of Morse-Smale flows, admitting the presence of ...
Added: November 27, 2020
Obukhov A., Проценко Л. М., Глазунова О. В. et al., Исследователь/Researcher 2020 № 1 С. 46–87
The program “Topos. Research in Local Studies” is a synthesis of the traditional approach of local historians and researchers and the modern ecosystem approach to the development of open educational environments, training of mentors and scientific leaders and the organization of modern youth’s local studies. The concept presents the basic principles and algorithms for organizing ...
Added: May 30, 2020
Obukhov A., Исследователь/Researcher 2019 № 4 С. 103–129
This article sets general principles of the realization of such format of participation in the research culture as an offcite research school. The general topos construct as a semantic model of organization of the content of the directions of research that are attached to common place is illustrated. The experience of the organization and conduction ...
Added: November 7, 2019
Obukhov A., Исследователь/Researcher 2019 № 4 С. 73–102
The article presents a justification, a description and examples of realization of the technology of the birth of the research idea on district. That technology allows from the very beginning of activity to bring students to the subject position during development of research culture. The technology is approbated more than 560 participants of different ages ...
Added: November 7, 2019
Obukhov A., Saveleva D. I., Исследователь/Researcher 2019 № 4 С. 12–47
On the initiative of the Moscow City Tourism Committee “The City of Discoveries” project was developed – to develop edu¬cational tourism for schoolchildren from Russian regions in Moscow as a living and developing megalopolis. This project is starting in a pilot mode at the end of 2019. The article presents the methodol¬ogy of the educational ...
Added: November 7, 2019
Kolobianina A., Kruglov V., Журнал Средневолжского математического общества 2019 Т. 21 № 4 С. 460–468
The paper is devoted to the study of the class of Ω-stable flows without limit cycles on
surfaces, i.e. flows on surfaces with non-wandering set consisting of a finite number of hyperbolic
fixed points. This class is a generalization of the class of gradient-like flows, differing by forbiddance
of saddle points connected by separatrices. The results of the ...
Added: October 22, 2019
Inkina S., , in: Global Encyclopedia of Public Administration, Public Policy, and Governance (Living Edition).: Cham: Springer, 2019. P. 1–10.
This work serves as a comprehensive collection of global scholarship regarding the vast fields of public administration and public policy. Written and edited by leading international scholars and practitioners, this exhaustive resource covers all areas of the twin fields of study. In keeping with the multidisciplinary spirit of these fields, the entries make use of ...
Added: September 18, 2018
Босова А. А., Kruglov V., Pochinka O., Таврический вестник информатики и математики 2017 № 4(37) С. 51–58
In this paper the class of simplest not rough Ω-stable flows on a sphere is considered. We call simplest not rough Ω-stable flow an Ω-stable flow with least number of fixed points, a single separatrix connecting saddle points and without limit cycles. For such flows we design the Morse energy function. ...
Added: March 9, 2018
Vladislav Kruglov, Dmitry Malyshev, Olga Pochinka, Discrete and Continuous Dynamical Systems 2018 Vol. 38 No. 9 P. 4305–4327
Structurally stable (rough) flows on surfaces have only finitely many singularities and nitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads to Ω-stable flows on surfaces, which are not structurally stable. However, in the present paper we prove that a ...
Added: October 2, 2017
Kruglov V., Malyshev D., Pochinka O., Математический сборник 2018 Т. 209 № 1 С. 100–126
Изучение динамики потока на поверхностях путем разбиения фазового пространства на ячейки с одинаковым предельным поведением траекторий внутри ячейки восходит к классическим работам А.А. Андронова, Л.С. Понтрягина, Е.А. Леонтович, А. Г. Майера. Типы ячеек, которых конечное число, и их примыкание друг к другу полностью определяют класс топологической эквивалентности потока с конечным числом особых траекторий. Если в ...
Added: September 11, 2017
Vladislav E. Kruglov, Dmitry S. Malyshev, Olga V. Pochinka, / Series math "arxiv.org". 2017. No. 1706.01695v1.
Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads to Ω-stable flows on surfaces, which are not structurally stable. However, in the present paper we prove that a ...
Added: September 11, 2017