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arXiv · 1803.05966

On entropy and intrinsic ergodicity of coded subshifts

Ronnie Pavlov
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Abstract

Any coded subshift X defined by a set C of code words contains a subshift, which we call L, consisting of limits of single code words. We show that when C satisfies a unique decomposition property, the topological entropy h(X) of X is determined completely by h(L) and the number of code words of each length. More specifically, we show that h(X) = h(L) exactly when a certain infinite series is less than or equal to 1, and when that series is greater than 1, we give a formula for h(X_C). In the latter case, an immediate corollary (using results of Climenhaga and Thompson) is that X has a unique measure of maximal entropy.

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Ronnie Pavlov. 2018-03-15. On entropy and intrinsic ergodicity of coded subshifts. https://arxiv.org/abs/1803.05966

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