Bowen's equations for invariance pressure of control systems

Rui Yang; Ercai Chen; Jiao Yang; Xiaoyao Zhou

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arXiv · 2309.01628

Bowen's equations for invariance pressure of control systems

Rui Yang·Ercai Chen·Jiao Yang·Xiaoyao Zhou

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Abstract

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.

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BibTeX RIS

Rui Yang, Ercai Chen, Jiao Yang, Xiaoyao Zhou. 2023-09-04. Bowen's equations for invariance pressure of control systems. https://arxiv.org/abs/2309.01628

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