# Equivalent subshifts

Let $X$ be a finite set, $(X^{\mathbb Z}, T)$ is the shift, i.e. the Tikhonov topological space of all bi-infinite words in $X$, $T$ shifts the words one letter to the right. A subshift is a closed subset of $X^{\mathbb{Z}}$ stable under $T$.
Is there a recent survey about the problem of equivalence of subshifts?

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In what sense "equivalencve"? There are several notions ranging from conjugacy to orbit equivalence. –  SIB Apr 29 '11 at 16:28
@SIB: In all possible senses. I know of some versions and would like, in particular, to know about the others. –  Mark Sapir Apr 29 '11 at 16:38