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 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.

KEYWORDS:

• Topological pressure dimension
• almost additive sequence
• topological entropy dimension

2010 Mathematics Subject Classification:

• 54H20
• 37B20

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.

Additional information

Funding

The work was supported by the Fundamental Research Funds for the Central Universities [grant number WK0010000035]; the National Natural Science Foundation of China [grant number 11401363]; China Postdoctoral Science Foundation [grant number 2015M580728]; Shenzhen University Foundation [grant number 201462].