In this paper, we give the definition of unstable topological entropy in mean u-metrics (the mean metrics in the unstable manifold) for partially hyperbolic systems. By establishing Katok's entropy formula of unstable metric entropy in mean u-metrics, we prove that the new unstable topological entropy is equal to the unstable topological entropy defined in Bowen u-metrics (the Bowen metrics in the unstable manifold). Finally, we obtain the variational principle related to the unstable topological entropy defined in mean u-metrics and unstable metric entropy, which states that the unstable topological entropy defined in mean u-metrics is the supremum of the unstable metric entropy taken over all invariant measures.

在本文中，我们给出了部分双曲系统的均值u度量（不稳定流形中的平均度量）中不稳定拓扑熵的定义。通过建立均值u -metrics中不稳定度量熵的 Katok 熵公式，我们证明了新的不稳定拓扑熵等于 Bowen u -metrics 中定义的不稳定拓扑熵（不稳定流形中的 Bowen 度量）。最后，我们获得有关平均定义的不稳定拓扑熵变分原理ü -度量和不稳定的度量熵，其中指出，在均值U型指标定义的不稳定拓扑熵是接管一切不变测度不稳定度量熵确.