Abstract In this paper, unstable metric entropy, unstable topological entropy and unstable pressure for partially hyperbolic endomorphisms are introduced and investigated. A version of Shannon-McMillan-Breiman Theorem is established, and a variational principle is formulated, which gives a relationship between unstable metric entropy and unstable pressure (unstable topological entropy). As an application of the variational principle, some results on the u-equilibrium states are given.

中文翻译：

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部分双曲自同态的不稳定熵和不稳定压力

摘要 本文介绍并研究了部分双曲自同态的不稳定度量熵、不稳定拓扑熵和不稳定压力。建立了香农-麦克米兰-布赖曼定理的一个版本，并制定了变分原理，该原理给出了不稳定度量熵和不稳定压力（不稳定拓扑熵）之间的关系。作为变分原理的应用，给出了一些关于u平衡态的结果。