Сценарий изменения гомотопического типа замыкания инвариантного седлового многообразия.
Журнал Средневолжского математического общества. 2020. Т. 22. № 3. С. 306-318.
, , Journal of Mathematical Sciences 2020 No. 250 P. 94-108
We consider the class of gradient-like diffeomorphisms possessing an attractor and a repeller separated by a circle on a 2-sphere. For any diffeomorphism in this class we construct a stable arc connecting it with the source-sink system. ...
Added: November 18, 2020
, Динамические системы 2020 Vol. 10(38) No. 2 P. 139-148
In this paper, a class of gradient-like diffeomorphisms $f$ on a closed orientable surface is considered, under the assumption that all non-wandering points of $f$ are fixed and have a positive orientation type. The main result is a construction of a stable arc joining two such diffeomorphisms. The diffeomorphisms under the consideration are Palis diffeomorphisms, ...
Added: February 13, 2021
, , Проблемы математического анализа 2020 № 104 С. 85-98
A class of gradient-like diffeomorphisms with an attractor and a repeller separated by a circle on a two-sphere is considered. For any diffeomorphism of this class, a stable arc is constructed connecting it to the source-sink system. ...
Added: November 11, 2020
Solution of the 33rd Palis-Pugh problem for gradient-like diffeomorphisms of a two-dimensional sphere
, , Discrete and Continuous Dynamical Systems 2021 Vol. 41 No. 3 P. 1101-1131
In the present paper, a solution to the 33rd Palis-Pugh problem for gradient-like diffeomorphisms of a two-dimensional sphere is obtained. It is precisely shown that with respect to the stable isotopic connectedness relation there exists countable many of equivalence classes of such systems. ...
Added: November 11, 2020
, , Russian Journal of Nonlinear Dynamics 2021 Vol. 17 No. 1 P. 23-37
The problem of the existence of an arc with at most countable (finite) number of bifurcations connecting structurally stable systems (Morse – Smale systems) on manifolds was included in the list of fifty Palis – Pugh problems at number 33. In 1976 S. Newhouse, J.Palis, F.Takens introduced the concept of a stable arc connecting two structurally ...
Added: April 19, 2021
О бифуркациях, меняющих гомотопический тип замыкания инвариантного седлового многообразия диффеоморфизма поверхности
, , Математический сборник 2022 Т. 213 № 3 С. 81-110
It is well known from the homotopy theory of surfaces that an ambient isotopy does not change the homotopy type of a closed curve. Using the language of dynamical systems, this means that an arc in the space of diffeomorphisms that joins two isotopic diffeomorphisms with invariant closed curves in distinct homotopy classes must go ...
Added: May 21, 2022
, , Technische Mechanik 2017 Vol. 37 No. 2-5 P. 129-138
Dynamics of a massive point on a rotating wire or surface under dry friction force action is considered. Existence, stability and bifurcations of non-isolated relative equilibria sets of the point located - on a sphere uniformly rotating about an inclined fixed axis; - on a thin circular hoop rotating about an inclined fixed axis; - ...
Added: December 7, 2017
, , , Журнал Средневолжского математического общества 2013 Т. 15 № 1 С. 76-79
Приводятся бифуркации разрушения и рождения соленоидов Смейла-Вильямса ...
Added: October 17, 2014
, , Огарев-online. Россия. 2016 № 20
The paper studies a one-parametric family of trajectories of points in the Reuleaux triangle formed by its rolling within a square. The bifurcation values that determine the qualitative behavior of the trajectory are found. The trajectory components, their number and equations are determined. For all values that are greater than the first bifurcation value a ...
Added: November 19, 2016
, , Журнал вычислительной математики и математической физики 2020 Т. 60 № 8 С. 1291-1303
The importance of functional differential equations of pointwise type is determined by the fact that their solutions are used to construct traveling-wave solutions for induced infinite-dimensional ordinary differential equations, and vice versa. Solutions of such equations exhibit bifurcation. A theorem on branching bifurcation is obtained for the solution to a linear homogeneous functional differential equation ...
Added: August 25, 2020
, , Научно-технические ведомости Санкт-Петербургского государственного политехнического университета. Экономические науки 2014 № 2(192) С. 200-205
This article discusses examples of nonlinear models of economic dynamics and possibilities of their research by numerical procedures in MATLAB. Demonstrated specific effects of these models, in particular, the possibility of forming a chaotic behavior ...
Added: May 18, 2014
, , Успехи математических наук 2020 Т. 75 № 2 С. 195-196
The problem of the existence of an arc with no more than a countable (finite) number of bifurcations connecting structurally stable systems (Morse-Smale systems) on manifolds is included in the list of fifty Palis-Pugh problems at number 33. This article describes a solution to this problem for gradient-like diffeomorphisms of a two-dimensional sphere. ...
Added: October 18, 2019
, , , International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2014 Vol. 24 No. 8 P.
In the survey, we consider bifurcations of attracting (or repelling) invariant sets of some classical dynamical systems with a discrete time. ...
Added: September 11, 2014
, , Computational Mathematics and Mathematical Physics 2020 Vol. 60 No. 8 P. 1249-1260
The importance of functional differential equations of pointwise type is determined by the fact that their solutions are used to construct traveling-wave solutions for induced infinite-dimensional ordinary differential equations, and vice versa. Solutions of such equations exhibit bifurcation. A theorem on branching bifurcation is obtained for the solution to a linear homogeneous functional differential equation of pointwise type. ...
Added: September 21, 2020
On a class of isotopic connectivity of gradient-like maps of the 2-sphere with saddles of negative orientation type
, , et al., Russian Journal of Nonlinear Dynamics 2019 Vol. 15 No. 2 P. 199-211
We consider the class $G$ of gradient-like orientation preserving diffeomorphisms of the 2-sphere with saddles of negative orientation type. We show that the for every diffeomorphism $f\in G$ every saddle point is fixed. We show that there are exactly three equivalence classes (up to topological conjugacy) $G=G_1\cup G_2\cup G_3$ where a diffeomorphism $f_1\in G_1$ has ...
Added: June 24, 2019
, , , Нелинейная динамика 2017 Т. 13 № 4 С. 573-578
In this paper, one of the possible scenarios for the creation of heteroclinic separators in the solar corona is described and realized. This reconnection scenario connects the magnetic field with two zero points of different signs, the fan surfaces of which do not intersect, with a magnetic field with two zero points which are connected ...
Added: October 17, 2017
, , , Moscow Mathematical Journal 2019 Vol. 19 No. 4 P. 709-737
We classify global bifurcations in generic one-parameter local families of vector elds on S2 with a parabolic cycle. The classication is quite dierent from the classical results presented in monographs on the bifurcation theory. As a by product we prove that generic families described above are structurally stable. ...
Added: October 23, 2020
, , , Communications in Nonlinear Science and Numerical Simulation 2021 Vol. 93 Article 105525
Solitons and cavitons (the latter are localized solutions with singularities) for the nonlocal Whitham equations are studied. The fourth order differential equation for traveling waves with a parameter in front of the fourth derivative is reduced to a reversible Hamiltonian system defined on a two-sheeted four-dimensional space. Solutions of the system which stay on one ...
Added: September 16, 2020
, , , , in : 2020 4th Scientific School on Dynamics of Complex Networks and their Application in Intellectual Robotics (DCNAIR). : IEEE Xplore, 2020. P. 261-264.
Added: October 12, 2020
, , et al., , in : 66th International Astronautical Congress 2015 (IAC 2015): Space - The Gateway for Mankind's Future. Proceedings of a meeting held 12-16 October 2015, Jerusalem, Israel. : International Astronautical Federation, 2016.
We consider dynamics of a space elevator on an asteroid, i. e., spacecraft attached to a rotating celestial body with a light inextensible tether. We study the domains attainable for the spacecraft depending on such problem parameters as the angular velocity of the asteroid, the tether length, the position of the anchor at the surface, ...
Added: December 20, 2016
Macroeconomic Model with Monetary and Fiscal Policy and Externality: Nonlinear dynamics, Optimization and Control
, , et al., IFAC-PapersOnLine 2021 Vol. 54 No. 17 P. 26-31
Irregular fluctuations in economy lead to unpredictable effects and disrupt its stable functioning. Various tools could be used to stabilize irregular dynamics in economic models. For example, to introduce control into the model as an external function, as well as to take into account the internal characteristics of economic agents in the economy under consideration, ...
Added: February 5, 2022
, В кн. : Мир человека: неопределенность как вызов. : М. : ЛЕНАНД, 2019. Гл. 9. С. 111-124.
The article substantiates that uncertainties, instabilities, and fluctuations accompanying the development processes in the modern world not only create difficulties for us, but also form a basis for our individual and collective creativity. The future is open and not given to us in advance, and it is in the power of a man to make ...
Added: November 21, 2018
, , , Эффективное антикризисное управление 2015 № 2 (89) С. 84-92
Состояние глобальной экосистемы приближаетсяк критическому уровню, что отражается на социально-экономическом развитии общества. На современном этапе предметом изучения экономики и финансов должен стать анализ мира, для которого характерно нестационарное поведение, социально-экономические и экологические кризисы, связанные с нелинейностью и многомерностью социально-экономических систем. В статье построен комплекс моделей катастроф глобального социально-экономического развития. Для проведения анализа выбрана методология синергетики, которая основывается на теориисамоорганизации и коэволюции сложных ...
Added: June 22, 2015
, , , Regular and Chaotic Dynamics 2016 Vol. 21 No. 7-8 P. 885-901
This paper is concerned with the rolling motion of a dynamically asymmetric unbalanced ball (Chaplygin top) in a gravitational field on a plane under the assumption that there is no slipping and spinning at the point of contact. We give a description of strange attractors existing in the system and discuss in detail the scenario ...
Added: January 30, 2017