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Control Optim."],"published-print":{"date-parts":[[2025,4,30]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We aim to establish Bowen\u2019s equations for upper capacity invariance pressure and Pesin\u2013Pitskel 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\u2019s equation. In addition, to establish Bowen\u2019s equation for Pesin\u2013Pitskel invariance pressure on partitions, we introduce a new notion called the BS invariance dimension on subsets. 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