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.

**1.**J. Barral and D. J. Feng,*Weighted thermodynamic formalism and applications*(2009), arXiv:0909.4247v1.**2.**Ronald Meester and Jeffrey E. Steif,*Higher-dimensional subshifts of finite type, factor maps and measures of maximal entropy*, Pacific J. Math.**200**(2001), no. 2, 497–510. MR**1868699**, 10.2140/pjm.2001.200.497**3.**Anthony N. Quas and Paul B. Trow,*Subshifts of multi-dimensional shifts of finite type*, Ergodic Theory Dynam. Systems**20**(2000), no. 3, 859–874. MR**1764932**, 10.1017/S0143385700000468**4.**Bruce P. Kitchens,*Symbolic dynamics*, Universitext, Springer-Verlag, Berlin, 1998. One-sided, two-sided and countable state Markov shifts. MR**1484730****5.**François Ledrappier and Peter Walters,*A relativised variational principle for continuous transformations*, J. London Math. Soc. (2)**16**(1977), no. 3, 568–576. MR**0476995****6.**Peter Walters,*An introduction to ergodic theory*, Graduate Texts in Mathematics, vol. 79, Springer-Verlag, New York-Berlin, 1982. MR**648108****7.**Yun Zhao and Yongluo Cao,*On the topological pressure of random bundle transformations in sub-additive case*, J. Math. Anal. Appl.**342**(2008), no. 1, 715–725. MR**2440833**, 10.1016/j.jmaa.2007.11.044**8.**Yong-Luo Cao, De-Jun Feng, and Wen Huang,*The thermodynamic formalism for sub-additive potentials*, Discrete Contin. Dyn. Syst.**20**(2008), no. 3, 639–657. MR**2373208****9.**De-Jun Feng and Wen Huang,*Lyapunov spectrum of asymptotically sub-additive potentials*, Comm. Math. Phys.**297**(2010), no. 1, 1–43. MR**2645746**, 10.1007/s00220-010-1031-x

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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:
http://dx.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