Let ℱ be a C2 random partially hyperbolic dynamical system. For the unstable foliation, the corresponding unstable metric entropy, unstable topological entropy and unstable pressure via the dynamics of ℱ on the unstable foliation are introduced and investigated. A version of Shannon–McMillan–Breiman Theorem for unstable metric entropy is given, and a variational principle for unstable pressure (and hence for unstable entropy) is obtained. Moreover, as an application of the variational principle, equilibrium states for the unstable pressure including Gibbs u-states are investigated.

中文翻译：

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随机部分双曲线动力系统的不稳定熵和不稳定压力

让ℱ做一个C2随机部分双曲线动力系统。对于不稳定的叶理，相应的不稳定度量熵，不稳定拓扑熵和不稳定压力通过动力学ℱ对不稳定叶理进行了介绍和研究。给出了用于不稳定度量熵的 Shannon-McMillan-Breiman 定理的一个版本，并获得了不稳定压力（因此也用于不稳定熵）的变分原理。此外，作为变分原理的应用，包括吉布斯在内的不稳定压力的平衡状态你- 状态被调查。