# Bounds for Invariance Pressure

## TL;DR

This paper establishes bounds for invariance pressure in control systems, providing explicit formulas for hyperbolic linear systems and exploring applications to Lie groups and inner control sets.

## Contribution

It introduces bounds for invariance pressure in control sets and derives an explicit formula for hyperbolic linear control systems, extending to Lie groups and inner control sets.

## Key findings

- Upper bounds for invariance pressure in control sets with nonempty interior.
- Lower bounds for invariance pressure in sets with finite volume.
- Explicit formula for hyperbolic linear control systems.

## Abstract

This paper provides an upper for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume. In the special case of the control set of a hyperbolic linear control system in R^{d} this yields an explicit formula. Further applications to linear control systems on Lie groups and to inner control sets are discussed.