Class degree and measures of relative maximal entropy

Date

2011-03-16T15:24:18Z

Authors

Allahbakhshi, Mahsa

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Abstract

Given a factor code [pi] from a shift of finite type X onto an irreducible sofic shift Y, and a fully supported ergodic measure v on Y we give an explicit upper bound on the number of ergodic measures on X which project to v and have maximal entropy among all measures in the fiber [pi]-1{v}. This bound is invariant under conjugacy. We relate this to an important construction for finite-to-one symbolic factor maps.

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Keywords

Shift of finite type, Relative entropy, Hausdorff dimension, Maximal entropy, Class degree

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