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Measures of maximal relative entropy

Karl Petersen·Anthony Quas·Sujin Shin
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Abstract

Given an irreducible subshift of finite type X, a subshift Y, a factor map π: X \to Y, and an ergodic invariant measure νon Y, there can exist more than one ergodic measure on X which projects to νand has maximal entropy among all measures in the fiber, but there is an explicit bound on the number of such maximal entropy preimages.

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Karl Petersen, Anthony Quas, Sujin Shin. 2002-03-07. Measures of maximal relative entropy. https://arxiv.org/abs/math/0203072

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