23 citations · 42 across the 7 of their papers we have counts for
7 papers
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 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…
Dynamically ordered energy function for Morse-Smale diffeomorphisms on 3-manifolds
Viatcheslav Grines, Francois Laudenbach, Olga Pochinka
This note deals with arbitrary Morse-Smale diffeomorphisms in dimension 3 and extends ideas from \cite{GrLaPo}, \cite{GrLaPo1}, where gradient-like case was considered. We introduc…
Quasi-energy function for diffeomorphisms with wild separatrices
Viatcheslav Grines, Francois Laudenbach, Olga Pochinka
According to Pixton, there are Morse-Smale diffeomorphisms of the 3-sphere which have no energy function, that is a Lyapunov function whose critical points are all periodic points…
Self-indexing energy function for Morse-Smale diffeomorphisms on 3-manifolds
Viatcheslav Grines, Francois Laudenbach, Olga Pochinka
The paper is devoted to finding conditions to the existence of a self-indexing energy function for Morse-Smale diffeomorphisms on a 3-manifold. These conditions involve how the sta…
Essential curves in handlebodies and topological contractions
Viatcheslav Grines, François Laudenbach
If is a compact set, a {\it topological contraction} is a self-embedding such that the intersection of the successive images , , consists of one point. In dime…
On two-dimensional surface attractors and repellers on 3-manifolds
Viatcheslav Grines, Vladislav Medvedev, Evgeny Zhuzhoma
We show that if is an -diffeomorphism with a surface two-dimensional attractor or repeller and is a supporting surface for $ \mat…