31 citations · 44 across the 8 of their papers we have counts for
8 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…
On decomposition of ambient surfaces admitting A-diffeomorphisms with nontrivial attractors and repellers
V. Grines, D. Mints
It is well-known that there is a close relationship between the dynamics of diffeomorphisms satisfying the axiom and the topology of the ambient manifold. In the given article,…
Morse index of saddle equilibria of gradient-like flows on connected sums of
Vyacheslav Grines, Elena Gurevich, Sergiy Maksymenko
Let be either -sphere or a connected sum of finitely many copies of , . A flow on is called gradien…
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 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…
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…