Relative entropy functions for factor maps between subshifts

Shin, Sujin

doi:10.1090/S0002-9947-05-03943-7

Relative entropy functions for factor maps between subshifts
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Trans. Amer. Math. Soc. 358 (2006), 2205-2216 Request permission

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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