On synchronized non-sofic subshifts

Abstract

We show that a synchronized coded system $X$ is intrinsically ergodic of full support if and only if $h(Y)$, the topological entropy of $Y$, is less than $h(X)$ whenever $Y$ is a proper subsystem of $X$. We also show that like systems with specification property, SVGL's the non-mixing extension of systems with specification property, are intrinsically ergodic of full support. Moreover, we compute the entropy of the underlying graph of the Fischer cover of a synchronized system.

This paper has been withdrawn due to a flaw in Theorems 3.12 and 3.13

Cited by in corpus (1)

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