Geodesic
On topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers
Russian journal of nonlinear dynamics, Tome 10 (2014) no. 1, pp. 17-33

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a class of diffeomorphisms on 3-manifolds which satisfy S. Smale's axiom $A$ such that their nonwandering set consists of two-dimensional surface basic sets. Interrelation between dynamics of such diffeomorphism and topology of the ambient manifold is studied. Also we establish that each considered diffeomorphism is $\Omega$-conjugated with a model diffeomorphism of mapping torus. Under certain assumptions on asymptotic properties of two-dimensional invariant manifolds of points from the basic sets, we obtain necessary and sufficient conditions of topological conjugacy of structurally stable diffeomorphisms from the considered class.
Keywords: diffeomorphism, basic set, topological conjugacy, attractor, repeller. 
@article{ND_2014_10_1_a1,
     author = {Vyacheslav Z. Grines and Yulia A. Levchenko and Olga V. Pochinka},
     title = {On  topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers},
     journal = {Russian journal of nonlinear dynamics},
     pages = {17--33},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2014_10_1_a1/}
}
TY  - JOUR
AU  - Vyacheslav Z. Grines
AU  - Yulia A. Levchenko
AU  - Olga V. Pochinka
TI  - On  topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers
JO  - Russian journal of nonlinear dynamics
PY  - 2014
SP  - 17
EP  - 33
VL  - 10
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2014_10_1_a1/
LA  - ru
ID  - ND_2014_10_1_a1
ER  - 
%0 Journal Article
%A Vyacheslav Z. Grines
%A Yulia A. Levchenko
%A Olga V. Pochinka
%T On  topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers
%J Russian journal of nonlinear dynamics
%D 2014
%P 17-33
%V 10
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2014_10_1_a1/
%G ru
%F ND_2014_10_1_a1
Vyacheslav Z. Grines; Yulia A. Levchenko; Olga V. Pochinka. On  topological classification of diffeomorphisms on 3-manifolds with two-dimensional surface attractors and repellers. Russian journal of nonlinear dynamics, Tome 10 (2014) no. 1, pp. 17-33. http://geodesic.mathdoc.fr/item/ND_2014_10_1_a1/