Given a topological dynamical system (X,T), i.e., T is a continuous transformation on a compact metric space X), that admits mistakes and an invariant measure, this paper proves the Brin–Katok formula in this case. In particular, this paper finds that it suffices to study a mistake function which is linear in n and monotonic with respect to Δ. Consequently, this paper shows the Brin–Katok formula for the mean Bowen ball replacing the Bowen metrics with the mean Bowen metrics. The results presented in this paper may have some applications in the study of other properties of a dynamical system which admits small errors.

中文翻译：

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动力系统承认错误的 Brin-Katok 公式

给定一个拓扑动力系统( X,T )，即T是紧致度量空间X上的一个连续变换，它承认错误和一个不变测度，本文证明了这种情况下的Brin-Katok 公式。特别地，本文发现研究一个关于n线性且关于Δ单调的误差函数就足够了。因此，本文展示了平均 Bowen 球的 Brin-Katok 公式，用平均 Bowen 度量替换了 Bowen 度量。本文中提出的结果可能在研究允许小误差的动力系统的其他特性方面有一些应用。