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arXiv · 1911.10234

On Topological Classification of Morse-Smale Diffeomorphisms on the Sphere $S^n$

Vyachesval Grines·Elena Gurevich·Olga Pochinka·Dmitrii Malyshev
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Abstract

We consider a class $G(S^n)$ of orientation preserving Morse-Smale diffeomorphisms of the sphere $S^{n}$ of dimension $n>3$ in assumption that invariant manifolds of different saddle periodic points have no intersection. We put in a correspondence for every diffeomorphism $f\in G(S^n)$ a colored graph $Γ_f$ enriched by an automorphism $P_f$. Then we define the notion of isomorphism between two colored graphs and prove that two diffeomorphisms $f, f'\in G(S^n)$ are topologically conjugated iff the graphs $Γ_f$, $Γ_f'$ are isomorphic. Moreover we establish the existence of a linear-time algorithm for distinguishing two colored graphs of diffeomorphisms from the class $G(S^n)$.

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Vyachesval Grines, Elena Gurevich, Olga Pochinka, Dmitrii Malyshev. 2019-12-27. On Topological Classification of Morse-Smale Diffeomorphisms on the Sphere $S^n$. https://doi.org/10.1088/1361-6544%2Fabaf60

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