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Of all publications in the section: 55
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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.

Article
Сироткин Д. В. Журнал Средневолжского математического общества. 2018. Т. 20. № 2. С. 199-205.

The vertex 3-colourability problem is to determine for a given graph whether one can divide its vertex set into three subsets of pairwise non-adjacent vertices. This problem is NP-complete in the class of planar graphs, but it becomes polynomial-time solvable for planar triangulations, i.e. planar graphs, all facets of which (including external) are triangles. Additionally, the problem is NP-complete for planar graphs whose vertices have degrees at most 4, but it becomes linear-time solvable for graphs whose vertices have maximal degree at most 3. So it is an interesting question to nd a threshold for lengths of facets and maximum vertex degree, for which the complexity of the vertex 3-colourability changes from polynomial-time solvability to NP-completeness. In this paper we answer this question and prove NP-completeness of the vertex 3-colourability problem in the class of planar graphs of the maximum vertex degree at most 5, whose facets are triangles and quadrangles only.

Article
Жужома Е. В., Починка О. В., Гринес В. З. и др. Журнал Средневолжского математического общества. 2014. Т. 16. № 1. С. 8-16.
Article
Жужома Е. В., Гринес В. З., Медведев В. С. Журнал Средневолжского математического общества. 2013. Т. 15. № 3. С. 21-28.
Article
Куренков Е. Д. Журнал Средневолжского математического общества. 2017. Т. 19. № 1. С. 60-66.

In the article we construct an axiom $A$ endomorphism $f$ of 2-torus with nonwondering set that contains one-dimensional contracting repeller satisfying following properties:

1) $f(\Lambda)= \Lambda$, $f^{-1}(\Lambda)= \Lambda$;

2) $\Lambda$ is locally homeomorphic to the product of the Cantor set and the interval;

3) $T^2\setminus\Lambda$ consist of a countable family of disjoint open disks.

The key idea of construction consists in applying the surgery introduced by S.~Smale~\cite{Sm} to an algebraic endomorphism of the two-torus. We present the results of computational experiment that demonstrate correctness of our construction. Suggested construction reveals significant difference between one-dimensional basic of endomorphisms and one-dimensional basic sets of corresponding diffoemorphisms. In particular, the result contrasts with the fact that wondering set of axiom $A$ diffeomorphism consist of a finite number of open disks in case of spaciously situated basic set.

Article
Гуревич Е. Я., Сахаров А. Н., Трегубова Е. В. Журнал Средневолжского математического общества. 2013. Т. 15. № 4. С. 91-100.
Article
Гуревич Е. Я., Малышев Д. С. Журнал Средневолжского математического общества. 2016. Т. 18. № 4. С. 30-33.

We consider a  class  $G$ of orientation  preserving Morse-Smale diffeomorphisms without heteroclinical intersection defined  on the sphere $S^{n}$ of dimension  $n>3$. We put a colored graph $\Gamma_f$, endowed by a automorphism  $P_f$ into the correspondence for every diffeomorphism  $f\in G$ and give a definition of an isomorphism of such graphs. There is stated that there existence of isomorphism of graphs $\Gamma_f, \Gamma_{f'}$ is the neccesary and sufficient condition of topological conjugacy of diffeomorphisms $f, f'\in G$, and the exists an algorithm  recognizing the existence of the isomorphism of such graphs by linear time.

Article
Гуревич Е. Я., Куренков Е. Д. Журнал Средневолжского математического общества. 2014. Т. 16. № 3. С. 36-40.

We introduce the denition of consistent equivalence of Meyer ξ -functions for Morse- Smale ows on surfaces (that are Lyapunov funñtions) and state that consistent equivalence of ξ -functions is necessary and sucient condition for such ows.

Article
Митрякова Т., Починка О. В. Журнал Средневолжского математического общества. 2014. Т. 16. № 2. С. 76-79.

In present paper we consider a class of 3-manifolds' diffeomorphisms lying on the border of a set of gradient-like systems and different from the last not more than one tangencies' orbits of two-dimensional separatrices. It is proved that for studying diffeomorphisms necessary and sufficient condition for topological conjugacy of two diffeomorphisms from this class is a coincidence of classes of equivalence of their schemes and moduli of stability corresponding tangencies' orbits.}{Topological conjugacy, heteroclinic tangencies, moduli of stability.

Article
Круглов В. Е. Журнал Средневолжского математического общества. 2018. Т. 20. № 4. С. 419-428.

In 1978 J. Palis invented continuum topologically non-conjugate systems in a neighbourhood of a system with a heteroclinic contact (moduli). W. de Melo and С. van Strien in 1987 described a diffeomorphism class with a finite number of moduli: a chain of saddles taking part in the heteroclinic contact of such diffeomorphism includes not more than three saddles. Surprisingly, such effect does not happen in flows. Here we consider gradient flows of the height function for an orientable surface of genus g>0. Such flows have a chain of 2g saddles. We found that the value of moduli for such flows is 2g-1 which is the straight consequence of the sufficient topological conjugacy conditions for such systems given in our paper. A complete topological equivalence invariant for such systems is four-colour graph carrying the information about its cells relative position. Equipping the graph's edges with the analytical parameters -- moduli, connected with the saddle connections, gives the sufficient conditions of the flows topological conjugacy.

Article
Малышев Д. С. Журнал Средневолжского математического общества. 2020. Т. 22. № 1. С. 38-47.
Article
Гринес В. З., Куренков Е. Д. Журнал Средневолжского математического общества. 2018. Т. 20. № 2. С. 159-174.

The present paper is devoted to the topological classification of one-dimensional basiс sets of diffeomorphisms satisfying ещ the Smale's axiom A and given on orientable surfaces of negative Euler characteristic equipped with a metric of constant negative curvature. Using Lobachevsky's methods of geometry, each perfect one-dimensional attractor of A-diffeomorphism is uniquely associated with a geodesic lamination on the surface. It is established that, in the absence of special pairs of boundary periodic points in the attractor, there exists a homeomorphism of the surface homotopic to the identity that maps unstable manifolds of the points of the basic set into leaves of the geodesic lamination. Moreover, from the method of constructing geodesic laminations it follows that if the diffeomorphisms whose non-wandering sets contain perfect spaciously situated attractors are homotopic, then the geodesic laminations corresponding to these attractors coincide.

Article
Починка О. В., Романов А. Журнал Средневолжского математического общества. 2013. Т. 15. № 3. С. 120-125.
Article
Гонченко С., Исаенкова Н., Жужома Е. В. Журнал Средневолжского математического общества. 2013. Т. 15. № 1. С. 76-79.
Article
Гуревич Е. Я., Сяинова Д. Т. Журнал Средневолжского математического общества. 2014. Т. 16. № 2. С. 46-56.

We specify S. Batterson's results of [7] where classes of isotopic maps on torus contained Morse-Smale diffeomorphisms are described. Following to ideas of paper [7], we describe isotopic classes, contained gradient-like diffeomorphisms, present all admitted types of periodic data of such diffeomorphisms and provide an algorithm of realization of each type of periodic data.

Article
Жукова Н. И. Журнал Средневолжского математического общества. 2017. Т. 19. № 4. С. 33-44.

For any smooth orbifold $\mathcal N$ is constructed a foliated model, which is a foliation with an Ehresmann, the leaf space of which is the same as $\mathcal N$. We investigate the relationship  relationship between some properties of orbifold and its foliated model. The article discusses the application to Cartan orbifolds, that is orbifolds endowed with Cartan geometry.

Article
Грибанов Д. В., Малышев Д. С. Журнал Средневолжского математического общества. 2016. Т. 18. № 3. С. 19-31.
Article
Починка О. В., Ноздринова Е. В., Колобянина А. Е. Журнал Средневолжского математического общества. 2018. Т. 20. № 4. С. 408-418.

Mathematician A.G. Mayer from Nizhny Novgorod was the first who classify rough diffeomorphisms on a circle. This was one of the pioneering works on the topological classification of dynamic systems. However, the classification results in the work of A.G. Mayer obviously did not stand out, they were part of the proof of the roughness and genericity of Morse-Smale diffeomorphisms on a circle, and the realization problem was not solved. In the present work, the authors, as successors of the Nizhny Novgorod school of nonlinear oscillations, present a solution to the problem of the topological classification of rough transformations of a circle in a canonical formulation using modern methods and approaches. Namely, in the first theorem the type of periodic data of rough transformations of the circle is established, in the second theorem there are necessary and sufficient conditions for their conjugation, in the third theorem an admissible set of parameters is realized by a rough transformation of the circle