Topological pressure dimension for almost additive potentials

TL;DR

This paper explores the concept of topological pressure dimension for almost additive sequences, extending the idea of topological entropy dimension and analyzing its properties and relationships.

Contribution

It introduces the topological pressure dimension for almost additive sequences and investigates its fundamental properties and relationships, including inequalities and special cases.

Findings

Topological pressure dimension extends topological entropy dimension.

The pressure dimension satisfies certain inequalities.

It is always ≥ 1 for specific almost additive sequences.

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.