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 $\Gamma_f$ 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 $\Gamma_f$, $\Gamma_f'$ are isomorphic. Moreover we establish the existence of a linear-time algorithm for distinguishing two colored graphs of diffeomorphisms from the class $G(S^n)$.

中文翻译：

---

关于球体 S n (n > 3) 上 Morse-Smale 微分同胚的拓扑分类

我们考虑一个类$G(S^n)$ 的方向保持Morse-Smale 微分同胚，维度$n>3$ 的球体$S^{n}$，假设不同鞍周期点的不变流形没有交集。我们为每个微分同胚 $f\in G(S^n)$ 放置了一个对应关系，即一个由自同构 $P_f$ 丰富的彩色图 $\Gamma_f$。然后我们定义两个彩色图之间的同构概念，并证明两个微分同构 $f, f'\in G(S^n)$ 是拓扑共轭的，当当这些图 $\Gamma_f$, $\Gamma_f'$ 是同构的。此外，我们建立了线性时间算法的存在，用于从类 $G(S^n)$ 中区分两个微分同胚的彩色图。