Topological pressure dimension for almost additive potentials

Abstract

This paper is devoted to the study of the topological pressure dimension for almost additive sequences, which is an extension of topological entropy dimension. We investigate fundamental properties of the topological pressure dimension for almost additive sequences. In particular, we study the relationships among different types of topological pressure dimension and identifies an inequality relating them. Also, we show that the topological pressure dimension is always equal to or greater than 1 for certain special almost additive sequence.