On entropy and intrinsic ergodicity of coded subshifts

Pavlov, Ronnie

doi:10.1090/proc/15145

On entropy and intrinsic ergodicity of coded subshifts
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Proc. Amer. Math. Soc. 148 (2020), 4717-4731 Request permission

Abstract:

Any coded subshift $X_C$ defined by a set $C$ of code words contains a subshift, which we call $L_C$, consisting of limits of single code words. We show that when $C$ satisfies the unique decipherability property, the topological entropy $h(X_C)$ of $X_C$ is determined completely by $h(L_C)$ and the number of code words of each length. More specifically, we show that $h(X_C) = h(L_C)$ 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 a result from [Israel J. Math. 192 (2012), pp. 785–817] is that $X_C$ has a unique measure of maximal entropy.

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