Geodesic
Necessary and sufficient conditions for topological classification of Morse--Smale cascades on 3-manifolds
Russian journal of nonlinear dynamics, Tome 7 (2011) no. 2, pp. 227-238

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

In this paper class $MS(M^3)$ of Morse–Smale diffeomorphisms (cascades) given on connected closed orientable $3$-manifolds are considered. For a diffeomorphism $f\in MS(M^3)$ it is introduced a notion scheme $S_f$, which contains an information on the periodic data of the cascade and a topology of embedding of the sepsrstrices of the saddle points. It is established that necessary and sufficient condition for topological conjugacy of diffeomorphisms $f,f'\in MS(M^3)$ is the equivalence of the schemes $S_f$, $S_{f'}$.
Keywords: Morse–Smale diffeomorphism (cascade), topological conjugacy
Mots-clés : space orbit. 
@article{ND_2011_7_2_a2,
     author = {O. V. Pochinka},
     title = {Necessary and sufficient conditions for topological classification of {Morse--Smale} cascades on 3-manifolds},
     journal = {Russian journal of nonlinear dynamics},
     pages = {227--238},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ND_2011_7_2_a2/}
}
TY  - JOUR
AU  - O. V. Pochinka
TI  - Necessary and sufficient conditions for topological classification of Morse--Smale cascades on 3-manifolds
JO  - Russian journal of nonlinear dynamics
PY  - 2011
SP  - 227
EP  - 238
VL  - 7
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ND_2011_7_2_a2/
LA  - ru
ID  - ND_2011_7_2_a2
ER  - 
%0 Journal Article
%A O. V. Pochinka
%T Necessary and sufficient conditions for topological classification of Morse--Smale cascades on 3-manifolds
%J Russian journal of nonlinear dynamics
%D 2011
%P 227-238
%V 7
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ND_2011_7_2_a2/
%G ru
%F ND_2011_7_2_a2
O. V. Pochinka. Necessary and sufficient conditions for topological classification of Morse--Smale cascades on 3-manifolds. Russian journal of nonlinear dynamics, Tome 7 (2011) no. 2, pp. 227-238. http://geodesic.mathdoc.fr/item/ND_2011_7_2_a2/