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.

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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. 
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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/

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