Bowen's equations for invariance pressure of control systems

TL;DR

This paper develops Bowen's equations for various invariance pressures in discrete-time control systems, introducing new concepts like induced invariance pressure and BS invariance dimension, and establishing their relationships and variational principles.

Contribution

It introduces new invariance pressure concepts and establishes Bowen's equations and variational principles for control system invariance measures.

Findings

Relation between upper capacity and Pesin-Pitskel invariance pressures via Bowen's equation

Introduction of induced invariance pressure on partitions

Establishment of a variational principle for BS invariance dimension

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.