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Decomposition of infinite-to-one factor codes and uniqueness of relative equilibrium states. (arXiv:1705.00448v2 [math.DS] UPDATED)
来源于:arXiv
We show that an arbitrary factor map $\pi:X \to Y$ on an irreducible subshift
of finite type is a composition of a finite-to-one factor code and a class
degree one factor code. Using this structure theorem on infinite-to-one factor
codes, we then prove that any equilibrium state $\nu$ on $Y$ for a potential
function of sufficient regularity lifts to a unique measure of maximal relative
entropy on $X$. This answers a question raised by Boyle and Petersen (for lifts
of Markov measures) and generalizes the earlier known special case of
finite-to-one factor codes. 查看全文>>