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Построение энергетической функции для A-диффеоморфизмов с двумерным неблуждающим множеством на 3-многообразиях
Труды Средневолжского математического общества. 2015. Т. 17. № 3. С. 12-17.
Publication based on the results of:
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
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
Pochinka O., Митрякова Т. М., Grines V., Журнал Средневолжского математического общества 2013 Т. 15 № 4 С. 9-14
В настоящей работе устанавливается существование энергетической функции (гладкой функции Ляпунова, множество критических точек которой совпадает с неблуждающим множеством системы) у структурно устойчивых сохраняющих ориентацию диффеоморфизмов поверхностей с нетривиальными одномерными базисными множествами. ...
Added: March 25, 2014
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
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
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
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
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
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
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
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
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
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
Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016
The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...
Added: November 2, 2016
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253
Added: December 22, 2016
Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.
We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...
Added: September 29, 2019
Shiryaev A., Zhitlukhin M., Ziemba W., / SSRN. Series Social Science Research Network "Social Science Research Network". 2013.
We study the land and stock markets in Japan circa 1990. While the Nikkei stock average in the late 1980s and its -48% crash in 1990 is generally recognized as a financial market bubble, a bigger bubble and crash was in the golf course membership index market. The crash in the Nikkei which started on ...
Added: March 9, 2014
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016
Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291
The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...
Added: December 7, 2013
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
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
Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293
Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...
Added: September 29, 2014