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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Factor map, diamond and density of pressure functions
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by Jung-Chao Ban and Chih-Hung Chang PDF
Proc. Amer. Math. Soc. 139 (2011), 3985-3997 Request permission


Letting $\pi :X\rightarrow Y$ be a one-block factor map and $\Phi$ be an almost-additive potential function on $X,$ we prove that if $\pi$ has diamond, then the pressure $P(X,\Phi )$ is strictly larger than $P(Y,\pi \Phi )$. Furthermore, if we define the ratio $\rho (\Phi )=P(X,\Phi )/P(Y,\pi \Phi )$, then $\rho (\Phi )>1$ and it can be proved that there exists a family of pairs $\left \{ (\pi _{i},X_{i})\right \} _{i=1}^{k}$ such that $\pi _{i}:X_{i} \rightarrow Y$ is a factor map between $X_{i}$ and $Y$, $X_{i}\subseteq X$ is a subshift of finite type such that $\rho (\pi _{i},\Phi |_{X_{i}})$ (the ratio of the pressure function for $P(X_{i},\Phi |_{X_{i}})$ and $P(Y,\pi \Phi )$) is dense in $[1,\rho (\Phi )]$. 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
  • MR Author ID: 684625
  • Email:
  • Chih-Hung Chang
  • Affiliation: Department of Mathematics, National Central University, Taoyuan 32001, Taiwan
  • Email:
  • 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
  • © Copyright 2011 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 139 (2011), 3985-3997
  • MSC (2010): Primary 37D35; Secondary 37B10, 37A35, 28A78
  • DOI:
  • MathSciNet review: 2823044