轨道跟踪、$ω$ -极限集和极小性
Orbital shadowing, $ω$-limit sets and minimality
摘要：
设$X$是一个紧致的Hausdorff空间，具有一致性$\mathscr{U}$，$f \colon X \to X$是一个连续函数.对于$D \in \mathscr{U}$，$D$ -伪轨道是序列$(x_i)$，其中$(f(x_i),x_{i+1}) \in D$对于所有索引$i$。在本文中，我们表明，伪轨道陷阱$ω$ -极限集在规定的准确性的邻域后，一个统一的时间段。一个后果，这是一个推广的结果Pilyugin等人：每个系统都有第二个弱跟踪性质。作为进一步的应用，我们给出了极小系统的伪轨刻画，并证明了每一个极小系统都具有强的轨道跟踪性。
英文摘要：
Let $X$ be a compact Hausdorff space, with uniformity $\mathscr{U}$, and let $f \colon X \to X$ be a continuous function. For $D \in \mathscr{U}$, a $D$-pseudo-orbit is a sequence $(x_i)$ for which $(f(x_i),x_{i+1}) \in D$ for all indices $i$. In this paper we show that pseudo-orbits trap $ω$-limit sets in a neighbourhood of prescribed accuracy after a uniform time period. A consequence of this is a generalisation of a result of Pilyugin et al: every system has the second weak shadowing property. By way of further applications we give a characterisation of minimal systems in terms of pseudo-orbits and show that every minimal system exhibits the strong orbital shadowing property.
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