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Transactions of the American Mathematical Society

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Relative entropy functions for factor maps between subshifts


Author: Sujin Shin
Journal: Trans. Amer. Math. Soc. 358 (2006), 2205-2216
MSC (2000): Primary 37B10, 28D99; Secondary 28D20
DOI: https://doi.org/10.1090/S0002-9947-05-03943-7
Published electronically: December 20, 2005
MathSciNet review: 2197440
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Abstract: Let $ (X, S)$ and $ (Y, T)$ be topological dynamical systems and $ \pi : X \rightarrow Y$ a factor map. A function $ F \in C (X)$ is a compensation function for $ \pi$ if $ P (F + \phi \circ \pi ) = P (\phi)$ for all $ \phi \in C(Y)$. For a factor code between subshifts of finite type, we analyze the associated relative entropy function and give a necessary condition for the existence of saturated compensation functions. Necessary and sufficient conditions for a map to be a saturated compensation function will be provided.


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Additional Information

Sujin Shin
Affiliation: Department of Mathematics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea
Email: sjs@math.kaist.ac.kr

DOI: https://doi.org/10.1090/S0002-9947-05-03943-7
Keywords: Subshift, factor code, relative pressure, relative entropy, compensation function
Received by editor(s): September 12, 2003
Received by editor(s) in revised form: June 30, 2004
Published electronically: December 20, 2005
Additional Notes: This work was supported by grant No. R04-2002-000-00060-0 from the Basic Research Program of the Korea Science and Engineering Foundation.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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