Geodesic
On the topological classification of Morse-Smale diffeomorphisms on the sphere $S^n$ via colored graphs
Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 4, pp. 30-33

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

We consider a class $G$ of orientation-preserving Morse-Smale diffeomorphisms without heteroclinic intersections defined on the sphere $S^{n}$ of dimension $n>3$. For every diffeomorphism $f\in G$ corresponding colored graph $\Gamma_f$, endowed by a automorphism $P_f$, is found. We also give definition of isomorphism of such graphs. The result is stated that existing isomorphism of graphs $\Gamma_f, \Gamma_{f'}$ is the neccesary and sufficient condition of topological conjugacy of diffeomorphisms $f, f'\in G$, and thatan algorithm exists which recognizes this existence by linear time.
Keywords: structurally stable dynamical systems, Morse-Smale diffeomorphisms, topological classification, algorithm of recognizing an existence of an isomorphism of graphs. 
@article{SVMO_2016_18_4_a2,
     author = {E. Ya. Gurevich and D. S. Malyshev},
     title = {On the topological classification of {Morse-Smale} diffeomorphisms on the sphere  $S^n$ via  colored graphs},
     journal = {\v{Z}urnal Srednevol\v{z}skogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {30--33},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a2/}
}
TY  - JOUR
AU  - E. Ya. Gurevich
AU  - D. S. Malyshev
TI  - On the topological classification of Morse-Smale diffeomorphisms on the sphere  $S^n$ via  colored graphs
JO  - Žurnal Srednevolžskogo matematičeskogo obŝestva
PY  - 2016
SP  - 30
EP  - 33
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a2/
LA  - ru
ID  - SVMO_2016_18_4_a2
ER  - 
%0 Journal Article
%A E. Ya. Gurevich
%A D. S. Malyshev
%T On the topological classification of Morse-Smale diffeomorphisms on the sphere  $S^n$ via  colored graphs
%J Žurnal Srednevolžskogo matematičeskogo obŝestva
%D 2016
%P 30-33
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a2/
%G ru
%F SVMO_2016_18_4_a2
E. Ya. Gurevich; D. S. Malyshev. On the topological classification of Morse-Smale diffeomorphisms on the sphere  $S^n$ via  colored graphs. Žurnal Srednevolžskogo matematičeskogo obŝestva, Tome 18 (2016) no. 4, pp. 30-33. http://geodesic.mathdoc.fr/item/SVMO_2016_18_4_a2/