Packing topological pressure for amenable group actions

TL;DR

This paper establishes a variational principle for amenable packing topological pressure, explores inequalities under factor maps, and characterizes conditions for equality in systems with the almost specification property.

Contribution

It introduces the variational principle for amenable packing topological pressure and analyzes its behavior under factor maps and generic point sets.

Findings

Proved the variational principle for amenable packing topological pressure.

Derived inequalities for amenable packing pressure under factor maps.

Established conditions for equality in systems with the almost specification property.

Abstract

In this paper, we first prove the variational principle for amenable packing topological pressure. Then we obtain an inequality concerning amenable packing pressure for factor maps. Finally, we show that the equality about packing topological pressure of the set of generic points when the system satisfies the almost specification property, or $\mu$ is ergodic.