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Relative entropy functions for factor maps between subshifts
Authors:Sujin Shin
Affiliation:Department of Mathematics, Korea Advanced Institute of Science and Technology, Daejeon 305-701, South Korea
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.

Keywords:Subshift   factor code   relative pressure   relative entropy   compensation function
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