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与Pesin-Pitskel不变性压力的Bowen方程。首先引入一种新的不变性压力——关于划分的诱导不变性压力，它专门化于关于划分的上容量不变性压力，进而证明这两类不变性压力通过一个Bowen方程相关联。此外，为建立关于划分的Pesin-Pitskel不变性压力的Bowen方程，我们引入了关于子集的新概念——BS不变性维数。同时，建立了关于子集的BS不变性维数的变分原理。