AI 中文总结
从配对动力系统\((f,g)\)角度研究拓扑动力概念，通过特定条件简化阴影研究，以例子说明假设充分性，证明在特定条件下有阴影的\((f,g)\)对拓扑稳定。
AI 中文摘要
我们从配对动力系统\((f,g)\)的角度研究阴影和拓扑稳定性等经典拓扑动力概念，其中\(f\)和\(g\)是度量空间\(X\)上的一致等价映射。我们观察到若\(g\)是等度连续且与\(f\)可交换，则\((f,g)\)的阴影研究可简化为\(g^{-1}f\)的经典阴影研究，通过例子说明了这些假设的充分性。最后证明若\(f\)是相对紧致度量空间上的扩张同胚映射，则任何具有阴影的\((f,g)\)对都是拓扑稳定的。
英文摘要
We study the classical topological dynamical notions of shadowing and topological stability from a viewpoint of paired dynamical system $(f,g)$, where $f$ and $g$ are uniform equivalences on a metric space $X$. We observe that if $g$ is equicontinuous and commutes with $f$, then the study of shadowing for $(f,g)$ is reduced to the study of the classical shadowing for $g^{-1}f$. The fact that these assumptions are sufficient is justified through examples. Finally, we prove that if $f$ is an expansive homeomorphism on a relatively compact metric space, then any pair $(f,g)$ with shadowing is topologically stable.
