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Of all publications in the section: 48
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Article
Круглов В. Е., Починка О. В. Журнал Средневолжского математического общества. 2016. Т. 18. № 3. С. 41-48.
Article
Сироткин Д. В., Малышев Д. С. Журнал Средневолжского математического общества. 2019. Т. 21. № 2. С. 215-221.
Article
Жукова Н. И., Шеина К. И. Журнал Средневолжского математического общества. 2016. Т. 18. № 2. С. 30-40.

We find necessary and sufficient conditions for a foliation of codimension $q$ on $n$-dimensional manifold with transverse linear connection to admit a transverse invariant pseudo-Riemannian metric of a given signature which is parallel with the respect to the indicated connection. In particular, we obtain a criterion for a foliation with transverse linear connection to be Riemannian foliation.

Article
Е.В. Жужома, Исаенкова Н., В.С. Медведев Журнал Средневолжского математического общества. 2018. Т. 20. № 1. С. 23-29.

In the paper we construct some example of smooth dieomorphism of closed manifold. This dieomorphism has one-dimensional (in topological sense) basic set with stable invariant manifold of arbitrary nonzero dimension and the unstable invariant manifold of arbitrary dimension not less than two. The basic set has a saddle type, i.e. is neither attractor nor repeller. In addition, it follows from the construction that the dieomorphism has a positive entropy and is conservative (i.e. its jacobian equals one) in some neighborhood of the one-dimensional solenoidal basic set. The construction represented in this paper allows to construct a dieomorphism with the properties stated above on the manifold that is dieomorphic to the prime product of the circle and the sphere of codimension one

Article
Жужома Е. В., Медведев В. С. Журнал Средневолжского математического общества. 2017. Т. 19. № 2. С. 53-61.
Article
Жужома Е. В., Медведев В. С., Тарасова Н. Журнал Средневолжского математического общества. 2015. Т. 17. № 1. С. 55-65.
Article
Казаков А. О., Козлов А. Д. Журнал Средневолжского математического общества. 2018. Т. 20. № 2. С. 187-198.

In the paper a new method of constructing of three-dimensional flow systems with different chaotic attractors is presented. Using this method, an example of three-dimensional system possessing an asymmetric Lorenz attractor is obtained. Unlike the classical Lorenz attractor, the observed attractor does not have symmetry. However, the discovered asymmetric attractor, as well as classical one, belongs to a class of <<true>> chaotic, or, more precise, pseudohyperbolic attractors; the theory of such attractors was developed by D.~Turaev and L.P.~Shilnikov. Any trajectory of a pseudohyperbolic attractor has a positive Lyapunov exponent and this property holds for attractors of close systems. In this case, in contrast to hyperbolic attractors, pseudohyperbolic ones admit homoclinic tangencies, but bifurcations of such tangencies do not lead to generation of stable periodic orbits. In order to find the non-symmetric Lorenz attractor we applied the method of <<saddle chart>>. Using diagrams of maximal Lyapunov exponent, we show that there are no stability windows in the neighborhood of the observed attractor. In addition, we verify the pseudohyperbolicity for the non-symmetric Lorenz attractor using the LMP-method developed quite recently by Gonchenko, Kazakov and Turaev.

Article
Галкин О. Е., Галкина С. Ю. Журнал Средневолжского математического общества. 2019. Т. 21. № 4. С. 430-442.
Article
Гуревич Е. Я., Павлова Д. А. Журнал Средневолжского математического общества. 2018. Т. 20. № 4. С. 378-383.

We study a structure of four-dimensional phase space   decomposition on trajectories of  Morse-Smale flows admitting heteroclinical intersections.  We consider a class $G(S^4)$ of Morse-Smale flows on the sphere  $S^4$ such that for any flow  $f\in G(S^4)$ its non-wandering set consists of exactly four equilibria: source, sink and two saddles. Wandering set of such flows contains finite number of heteroclinical curves generating  the intersection of invariant manifolds of saddle equilibria.  We describe a topology of embedding of invariant manifolds of saddle equilibria  that is the first step in a solution of topological classification problem.

Article
Починка О. В., Ноздринова Е. В. Журнал Средневолжского математического общества. 2018. Т. 20. № 1. С. 30-38.

In this paper we consider a class Phi  of diffeomorphisms of a closed n -dimensional manifold that are bifurcation points of simple arcs in the space of diffeomorphisms. The authors have studied the asymptotic properties and the embedding structure of invariant manifolds of non-wandering points of such diffeomorphisms.

Article
Казаков А. О., Каратецкая Е. Ю., Сафонов К. А. и др. Журнал Средневолжского математического общества. 2019. Т. 21. № 4.

For three-dimensional dynamical systems with continuous time (flows), a classification of strange homoclinic attractors, which goes back to the papers S.V. Gonchenko, D.V. Turaev A.L. Shilnikov and L.P. Shilnikov, is proposed. By homoclinic we mean strange attractors containing a specific saddle equilibrium together with its unstable manifold. Moreover, the type of such an attractor is determined by the eigenvalues of the equilibrium. The classification of homoclinic attractors is based on a bifurcation analysis of systems of the form $\dot x=y+g_1(x,y,z), \dot y=z+g_2(x,y,z), \dot z=Ax+By+Cz+g_3(x,y,z), \;\; g_i(0,0,0) = (g_i)^\prime_x(0,0,0) = (g_i)^\prime_y(0,0,0) = (g_i)^\prime_z(0,0,0) = 0, \; i = 1, 2, 3$, whose linearization matrix is represented in the Frobenius form, and the eigenvalues are determined by the coefficients $A, B$ and $C$. In the parameters space $A, B$ and $C$, an extended bifurcation diagram is constructed, where 7 regions corresponding to attractors of various types are distinguished. It is noted that a wide class of three-dimensional flows can be reduced to the class of systems under consideration. The paper also discusses problems related to the pseudohyperbolicity of homoclinic attractors of three-dimensional flows (stability of chaotic dynamics to changes of system parameters). It is proved that in three-dimensional flows only two types of homoclinic attractors can be pseudo-hyperbolic: Lorenz-like attractors containing a saddle equilibrium state with a two-dimensional stable manifold whose saddle value is positive; as well as Shilnikov saddle attractors containing a saddle equilibrium with a two-dimensional unstable manifold.

Article
Починка О. В., Босова А. А. Журнал Средневолжского математического общества. 2019. Т. 21. № 2. С. 164-174.
Article
Круглов В. Е., Таланова Г. Н. Журнал Средневолжского математического общества. 2017. Т. 19. № 3. С. 31-40.

In this paper 2n-gons and surfaces obtained through identification of 2n-gon's sides in pairs (i.e. through sewing) are considered. As well-known, one can get surface of any genus and orientability through sewing but it's very uneasy to calculate by only the polygon and the way of sewing, because to do this one need to calculate the number of vertices appearing after identification; even for small n the problem is almost impossible if one want to do this directly. There are different ways to solve the task. The canonical variant of 4q-gon sewing (2q-gon sewing) giving an orientable (unorientable) surface of genus q is well-known, as the Harer-Zagier's numbers, that are the numbers of variants of sewing a 2n-gon to an orientable surface of gunes q. In this paper we offer a new way of Euler characteristic's of obtained surface calculation (and, hence, its genus) undepending on its orientability by means of three-colour graph and information about closed surfaces topological classification.

Article
Талецкий Д. С. Журнал Средневолжского математического общества. 2017. Т. 19. № 2. С. 105-116.
Article
Гуревич Е. Я. Журнал Средневолжского математического общества. 2017. Т. 19. № 2. С. 25-30.

This paper is the first step in stydying structure of decomposition of phase space with dimension n≥4" role="presentation" style="position: relative;">n≥4n≥4n\geq 4 on the trajectories of Morse-Smale flows (structurally stable flows with non-wandering set consisting of finite number of equilibria and closed trajectories) allowing heteroclinic intersections. More precisely, special class of Morse-Smale flows on the sphere Sn" role="presentation" style="position: relative;">SnSnSn is studied. The non-wandering set of the flow of interest consists of two nodal and two saddle equilibrium states. It is proved that for every flow from the class under consideration the intersection of invariant manifolds of two different saddle equilibrium states is nonempty and consists of a finite number of connectivity components. Heteroclinic intersections are mathematical models for magnetic field separators. Study of their structure, as well as the question of their existence, is one of the principal problems of magnetic hydrodynamics.

Article
Долгоносова А. Ю. Журнал Средневолжского математического общества. 2017. Т. 19. № 1. С. 19-29.

The subject of this article is a review of the results on foliations with transversal linear connection obtained by the author together with N.I. Zhukova, and their comparison with the results of other authors. The work consists of three parts. The first part focuses on to automorphism groups of foliations with a transversal linear connection in the category of foliations. In the second part, the question of the equivalence of the concept of completeness for the class of foliations under investigation is studied. The third part we present theorems on pseudo-Riemannian foliations that form an important class of foliations with a transversal linear connection.In particular, we present results on graphs of pseudo-Riemannian foliations that contain all information about foliations.