31 citations · 106 across the 27 of their papers we have counts for
27 papers
On homeomorphisms of three-dimensional manifolds with pseudo-Anosov attractors and repellers
Vyacheslav Grines, Olga Pochinka, Ekaterina Chilina
The present paper is devoted to a study of orientation-preserving homeomorphisms on three-dimensional manifolds with a non-wandering set consisting of a finite number of surface at…
Morse-Smale 3-diffeomorphisms with saddles of the same unstable manifold dimension
E. M. Osenkov, O. V. Pochinka
In this paper, we consider a class of Morse-Smale diffeomorphisms defined on a closed 3-manifold (non-necessarily orientable) under the assumption that all their saddle points have…
Classification of NMS-flows with unique twisted saddle orbit on orientable 4-manifolds
Vladislav Galkin, Olga Pochinka, Danila Shubin
Topological equivalence of Morse-Smale flows without fixed points (NMS-flows) under assumptions of different generalities was studied in a number of papers. In some cases when the…
On the topology of 3-manifolds admitting Morse-Smale diffeomorphisms with four fixed points of pairwise different Morse indices
O. Pochinka, E. Talanova
In the present paper we consider class of orientation preserving Morse-Smale diffeomorphisms , which defined on closed 3-manifold , and whose non-wandering set consist…
Links and dynamics
Valeriy Bardakov, Tatyana Kozlovskaya, Olga Pochinka
Knots naturally appear in continuous dynamical systems as flow periodic trajectories. However, discrete dynamical systems are also closely connected with the theory of knots and li…
Topology of Ambient 3-Manifolds of Non-singular Flows with Twisted Saddle Orbit
Olga Pochinka, Danila Shubin
In the present paper, non-singular Morse-Smale flows on closed orientable 3-manifolds under the assumption that among the periodic orbits of the flow there is only one saddle one a…
A quasi-energy function for Pixton diffeomorphisms defined by generalized Mazur knots
Timur Medvedev, Olga Pochinka
In this paper we give a lower estimate for the number of critical points of the Lyapunov function for Pixton diffeomorphisms (i.e. Morse-Smale diffeomorphisms in dimension 3 whose…
Characteristic space of orbits of Morse-Smale diffeomorphisms on surfaces
Elena Nozdrinova, Olga Pochinka, Ekaterina Tsaplina
The classical approach to the study of dynamical systems consists in representing the dynamics of the system in the form of a "source-sink", that means identifying an attractor-rep…
On classification of periodic maps on the 2-torus
D. Baranov, V. Grines, O. Pochinka +1
In this paper, following J.Nielsen, we introduce a complete characteristic of orientation preserving periodic maps on the two-dimensional torus. All admissible complete characteris…
There are no structural stable Axiom A 3-diffeomorphisms with dynamics "one-dimensional surfaced attractor-repeller"
Olga Pochinka
In this paper, we study the structural stability of three-dimensional diffeomorphisms with source-sink dynamics. Here the role of source and sink is played by one-dimensional hyper…
Nonsingular Morse-Smale flows of n-manifolds with attractor-repeller dynamics
Olga Pochinka, Danila Shubin
In the present paper the exhaustive topological classification of nonsingular Morse-Smale flows of -manifolds with two limit cycles is presented. Hyperbolicity of periodic orbit…
Stable arcs connecting polar cascades on a torus
E. V. Nozdrinova, O. V. Pochinka
In this paper, we obtain a solution to the 33rd Palis-Pugh problem for polar gradient-like diffeomorphisms on a two-dimensional torus, under the assumption that all non-wandering p…
Existence of an energy function for 3-dimensional chaotic "sink-source" cascades
M. Barinova, V. Grines, O. Pochinka +1
The paper is a continuation of research in the direction of energy function (a smooth Lyapunov function whose set of critical points coincides with the chain recurrent set of a sys…
On Topological Classification of Morse-Smale Diffeomorphisms on the Sphere
Vyachesval Grines, Elena Gurevich, Olga Pochinka +1
We consider a class of orientation preserving Morse-Smale diffeomorphisms of the sphere of dimension in assumption that invariant manifolds of different sadd…
On existence of a Morse energy function for topological flows with finite chain recurrent sets
Timur V. Medvedev, Olga V. Pochinka, Svetlana Kh. Zinina
We prove the existence of a continuous Morse energy function for an arbitrary topological flow with finite hyperbolic (in topological sense) chain recurrent set on a topological ma…
On embedding of arcs and circles in 3-manifolds in an application to dynamics of rough 3-diffeomorhisms with two-dimensional expanding attractor
Viacheslav Z. Grines, Evgeny V. Kruglov, Timur V. Medvedev +1
A topological classification of many classes of dynamical systems with regular dynamics in low dimensions is often reduced to combinatorial invariants. In dimension 3 combinatorial…
On Embedding of Multidimensional Morse-Smale Diffeomorphisms in Topological Flows
Vyacheslav Z. Grines, Elena Y. Gurevich, Olga V. Pochinka
J.~Palis found necessary conditions for a Morse-Smale diffeomorphism on a closed -dimensional manifold to embed into a topological flow and proved that these conditions ar…
A complete topological classification of Morse-Smale diffeomorphisms on surfaces: a kind of kneading theory in dimension two
V. Z. Grines, O. V. Pochinka, S. van Strien
In this paper we give a complete topological classification of orientation preserving Morse-Smale diffeomorphisms on orientable closed surfaces. For MS diffeomorphisms with relativ…
Topological classification of Morse-Smale diffeomorphisms on 3-manifolds
Ch. Bonatti, V. Grines, O. Pochinka
Topological classification of even the simplest Morse-Smale diffeomorphisms on 3-manifolds does not fit into the concept of singling out a skeleton consisting of stable and unstabl…
The wild Fox-Artin arc in invariant sets of dynamical systems
T. Medvedev, O. Pochinka
The modern qualitative theory of dynamical systems is thoroughly intertwined with the fairly young science of topology. Strange and even bizarre constructions of topology are found…
Topoligical classification of -stable flows on surfaces by means of effectively distinguishable multigraphs
Vladislav Kruglov, Dmitry Malyshev, Olga Pochinka
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 join…
Topological classification of Morse-Smale diffeomorphisms without heteroclinic curves on 3-manifolds
Ch Bonatti, V Grines, F Laudenbach +1
We show that, up to topological conjugation, the equivalence class of a Morse-Smale diffeomorphism without heteroclinic curves on 3-manifold is completely defined by an em- bedding…
On 2-diffeomorphisms with one-dimensional basic sets and a finite number of moduli
V. Z. Grines, O. V. Pochinka, S. Van Strien
This paper is a step towards the complete topological classification of Ω-stable diffeomorphisms on an orientable closed surface, aiming to give necessary and sufficient conditions…
On heteroclinic separators of magnetic fields in electrically conducting fluids
V. Grines, T. Medvedev, O. Pochinka +1
In this paper we partly solve the problem of existence of separators of a magnetic field in plasma. We single out in plasma a 3-body with a boundary in which the movement of plasma…