On the topological classification of Morse-Smale diffeomorphisms on the sphere $S^n$ via colored graphs
E. Gurevich1, D. Malyshev2
| Annotation | 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. |
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| Keywords | structurally stable dynamical systems, Morse-Smale diffeomorphisms, topological classification, algorithm of recognizing an existence of an isomorphism of graphs |
1Associate professor of Fundamental Mathematics Department, National Research University Higher School of Economics, egurevich@hse.ru
2Professor of Department of Applied Mathematics and Informatics, National Research University Higher School of Economics, Nizhny Novgorod; dsmalyshev@hse.ru
Citation: E. Gurevich, D. Malyshev, "[On the topological classification of Morse-Smale diffeomorphisms on the sphere $S^n$ via colored graphs]", Zhurnal Srednevolzhskogo matematicheskogo obshchestva,18:4 (2016) 30–33 (In Russian)
