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 identify 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.
Acknowledgements
The work was supported by the Fundamental Research Funds for the Central Universities (Grant No. WK0010000035), the National Natural Science Foundation of China (No. 11401363), China Postdoctoral Science Foundation (No. 2015M580728) and Shenzhen University Foundation (No. 201462). The authors are grateful to the anonymous referees for their comments, which helped to improve the text.
Disclosure statement
No potential conflict of interest was reported by the authors.