Factor map, diamond and density of pressure functions

Authors:
Jung-Chao Ban and Chih-Hung Chang

Journal:
Proc. Amer. Math. Soc. **139** (2011), 3985-3997

MSC (2010):
Primary 37D35; Secondary 37B10, 37A35, 28A78

Published electronically:
March 17, 2011

MathSciNet review:
2823044

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Abstract | References | Similar Articles | Additional Information

Abstract: Letting be a one-block factor map and be an almost-additive potential function on we prove that if has diamond, then the pressure is strictly larger than . Furthermore, if we define the ratio , then and it can be proved that there exists a family of pairs such that is a factor map between and , is a subshift of finite type such that (the ratio of the pressure function for and ) is dense in . This extends the result of Quas and Trow for the entropy case.

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Additional Information

**Jung-Chao Ban**

Affiliation:
Department of Mathematics, National Dong Hwa University, Hualien 970003, Taiwan

Email:
jcban@mail.ndhu.edu.tw

**Chih-Hung Chang**

Affiliation:
Department of Mathematics, National Central University, Taoyuan 32001, Taiwan

Email:
chchang@mx.math.ncu.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-2011-10803-7

Keywords:
Factor map,
diamond,
$\mathbf{a}$-weighted thermodynamic formalism,
density of pressure

Received by editor(s):
May 3, 2010

Received by editor(s) in revised form:
September 19, 2010

Published electronically:
March 17, 2011

Additional Notes:
The first author is partially supported by the National Science Council, ROC (Contract No. NSC 98-2628-M-259-001), National Center for Theoretical Sciences (NCTS) and CMPT (Center for Mathematics and Theoretical Physics) in National Central University.

The second author wishes to express his gratitude to Professor Cheng-Hsiung Hsu for his valuable comments and thanks the National Central University for financial support.

Communicated by:
Yingfei Yi

Article copyright:
© Copyright 2011
American Mathematical Society