Effective uniqueness of the measure of maximal entropy in Ornstein's d-metric
Vaughn Climenhaga, Teena Kumari
Abstract
Every topologically mixing shift of finite type has a unique measure of maximal entropy. It follows from Ornstein theory that every invariant measure with entropy close to maximal must be close to the MME in the d-metric. We prove a quantitative version of this, strengthening earlier results of Kadyrov that established effective uniqueness in the Wasserstein metric.
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