On synchronized non-sofic subshifts

arXiv1303.6570MaRDI QIDQ6240658

Dawoud Ahmadi Dastjerdi, S. Jangjooye Shaldehi

Publication date: 26 March 2013

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.

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