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Энергетическая функция для Ω-устойчивого потока с седловой связкой на сфере
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.
Pochinka O., Zinina S., Regular and Chaotic Dynamics 2021 Vol. 26 No. 4 P. 350-369
In this paper, we consider regular topological flows on closed n-manifolds. Such
flows have a hyperbolic (in the topological sense) chain recurrent set consisting of a finite number
of fixed points and periodic orbits. The class of such flows includes, for example, Morse – Smale
flows, which are closely related to the topology of the supporting manifold. This ...
Added: July 16, 2021
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
Kurenkov E., Gurevich E., Труды Средневолжского математического общества 2015 Т. 17 № 2 С. 15-26
We introduce the definition of consistent equivalence of energy Morse-Bott functions for Morse-Smale flows on surfaces and state that consistent equivalence of that functions is necessary and sufficient condition for such flows. ...
Added: October 12, 2015
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
Barinova M., Grines V., Pochinka O., Труды Математического института им. В.А. Стеклова РАН 2023 Т. 321 С. 45-61
C. Conley’s fundamental theorem of the theory of dynamical systems states that every dynamical system, even a nonsmooth one (i.e., a continuous flow or a discrete dynamical system generated by a homeomorphism), admits a continuous Lyapunov function. A Lyapunov function is strictly decreasing along the trajectories of the dynamical system outside the chain recurrent set ...
Added: September 7, 2023
Barinova M., Grines V., Pochinka O., Journal of difference equations and applications 2023 Vol. 29 No. 9-12 P. 1275-1286
In this paper, we consider a class of A-diffeomorphisms given on a 3-manifold, assuming that all the basic sets of the diffeomorphisms are two dimensional. It is known that such basic sets are either attractors or repellers and they are two types only, surface or expanding (contracting). One of the results of the paper is ...
Added: July 13, 2022
Gurevich E., Сахаров А. Н., Трегубова Е. В., Журнал Средневолжского математического общества 2013 Т. 15 № 4 С. 91-100
Работа является продолжением работы [#!gurevich-GrPoSaRu!#] и посвящена топологической классификации градиентно-подобных потоков, заданных на гладком замкнутом ориентируемом многообразии M n размерности n>3, с использованием энергетической функции. Рассмотрен класс G(M n)градиентно-подобных потоков без гетероклинических пересечений, все седловые состояния равновесия которых имеют индекс Морса 1 или (n-1). Показано, что необходимое и достаточное условие топологической эквивалентности потоков из класса G(M n) состоит в ...
Added: October 14, 2014
Grines V., Носкова М.К., Pochinka O., Динамические системы 2015 Т. 5 № 1-2 С. 31-37
В настоящей работе устанавливается существование энергетической функции для А-диффеоморфизмов, заданных на замкнутых ориентируемых двумерных многообразиях, не имеющих циклов и имеющих нетривиальные базисные множества только размерности один. Известно, что каждое базисное множество такого эндоморфизма является либо аттрактором, репеллером и локально устроено как декартово произведение канторова множества на интервал. Несмотря на сложную топологию неблуждающего множества, построенная энергетическая ...
Added: January 26, 2016
Pochinka O., Grines V., Носкова М.К., Труды Московского математического общества 2015 Т. 76 № 2 С. 271-286
В настоящей работе устанавливается существование энергетической функции структурно устойчивых диффеоморфизмов замкнутых трёхмерных многообразий, неблуждающее множество которых содержит двумерный растягивающийся аттрактор. ...
Added: October 12, 2015
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
Barinova M., Шустова Е. К., Журнал Средневолжского математического общества 2022 Т. 24 № 1 С. 21-30
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 ...
Added: April 1, 2022
Barinova M., Шустова Е. К., Журнал Средневолжского математического общества 2023 Т. 25 № 2 С. 11-21
This paper is devoted to the construction of an energy function, i.e. a smooth Lyapunov function, whose set of critical points coincides with the chain-recurrent set of a dynamical system — for a cascade that is a direct product of two systems. One of the multipliers is a structurally stable diffeomorphism given on a two-dimensional ...
Added: August 2, 2023
Barinova M., Lobachevskii Journal of Mathematics 2021 Vol. 42 No. 14 P. 3317-3323
If the chain recurrent set of a diffeomorphism f given on a closed n-manifold M^n is
hyperbolic (equivalently, f is an Ω-stable) then it coincides with the closure of the periodic points set
Perf and its chain recurrent components coincide with the basic sets. Due to C. Conley for such a
diffeomorphism there is a Lyapunov function which ...
Added: March 17, 2022
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
Grines V., Pochinka O., Современная математика. Фундаментальные направления 2017 Т. 63 № 2 С. 191-222
This review focuses on the presentation of results related to the energy function of discrete dynamical systems, as well as with the technique of constructing such functions for certain classes of Ω-stable and structurally stable diffeomorphisms on manifolds of dimension 2 and 3. ...
Added: September 5, 2017
Vladislav E. Kruglov, Dmitry S. Malyshev, Olga V. Pochinka, / Cornell University. 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
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
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019