BS Invariance Pressures for Control Systems

Three types of BS inner invariance pressures for control systems, as well as three versions of measure-theoretic BS inner invariance pressures, are introduced in this paper. We show that those BS inner invariance pressures are equivalent for the strongly invariant sets. Moreover, it is confirmed that they are the roots of Bowen’s equations for control systems. Then, we can further obtain an inverse variational principle for the measure-theoretic BS inner invariance pressure. Finally, a type of upper capacity BS invariance pressure and an explicit formula are presented for computing this invariance pressure of controlled invariant sets under some reasonable assumptions.