We aim to establish Bowen's equations for upper capacity invariance pressure and Pesin-Pitskel invariance pressure of discrete-time control systems. We first introduce a new invariance pressure called induced invariance pressure on partitions that specializes the upper capacity invariance pressure on partitions, and then show that the two types of invariance pressures are related by a Bowen's equation. Besides, to establish Bowen's equation for Pesin-Pitskel invariance pressure on partitions we also introduce a new notion called BS invariance dimension on subsets. Moreover, a variational principle for BS invariance dimension on subsets is established.

翻译：我们旨在建立离散时间控制系统的上容量不变性压力和Pesin-Pitskel不变性压力的Bowen方程。首先，我们引入一种新的不变性压力，即关于分划的诱导不变性压力，它专指关于分划的上容量不变性压力，并证明这两类不变性压力通过一个Bowen方程相关联。此外，为建立关于分划的Pesin-Pitskel不变性压力的Bowen方程，我们还引入了一个新概念——子集上的BS不变性维数。进一步地，我们建立了子集上的BS不变性维数的变分原理。