论文标题
阴影，拓扑熵和诱发的摩尔斯男友差异性的复发
Shadowing, topological entropy and recurrence of induced Morse-Smale diffeomorphisms
论文作者
论文摘要
令$ f：m \ rightarrow m $为在没有边界的紧凑型和连接的歧管上定义的摩尔斯 - 摩尔分型差异性。令$ c（m）$表示赋予Hausdorff公制的M的所有Subcontinua的超空间和$ c（f）：c（m）\ rightarrow c（m）$表示$ f $的同态同态。我们在本文中表明，如果$ m $是单位圆$ s^1 $，那么诱导的地图$ c（f）$就没有阴影属性。我们还表明，$ c（f）$的拓扑熵只有两个可能的值：$ 0 $或$ \ infty $。特别是，我们表明$ c（f）$的熵是$ 0 $当$ m $是单位圆$ s^1 $时，如果歧管$ m $的尺寸大于两个，则是$ \ infty $。此外，我们研究了诱导的地图$ 2^f $和$ c（f）$的复发，以及足够的条件，以获得超空间中无限拓扑熵。
Let $f : M \rightarrow M$ be a Morse-Smale diffeomorphism defined on a compact and connected manifold without boundary. Let $C(M)$ denote the hyperspace of all subcontinua of M endowed with the Hausdorff metric and $C(f) : C(M) \rightarrow C(M)$ denote the induced homeomorphism of $f$. We show in this paper that if $M$ is the unit circle $S^1$ then the induced map $C(f)$ has not the shadowing property. Also we show that the topological entropy of $C(f)$ has only two possible values: $0$ or $\infty$. In particular, we show that the entropy of $C(f)$ is $0$ when $M$ is the unit circle $S^1$ and it is $\infty$ if the dimension of the manifold $M$ is greater than two. Furthermore, we study the recurrence of the induced maps $2^f$ and $C(f)$ and sufficient conditions to obtain infinite topological entropy in the hyperspace.
