Topological conjugacy on the complement of the periodic points (Q441347)

For a subshift \(X\) denote by \(X^*\) the set of non-periodic sequences in \(X\). Subshifts \(X,Y\) are essentially conjugate if there exists a homeomorphism \(\phi : X^* \to Y^*\) which commutes with the shift map (restricted to respective subshifts), i.e. \(\sigma: \phi = \phi : \sigma\).NEWLINENEWLINEIf \(W\) is finite set of words, then \(X=W^\infty\) consisting of all bi-infinite sequences obtained as concatenation of these words is called a renewal system generated by \(W\).NEWLINENEWLINEThe authors provide a sufficient condition on \(W\) (so-called bounded generating set) when a renewal system generated by \(W\) is essentially conjugate to a shift of finite type. They also provide an example of a renewal system which is essentially conjugate but not conjugate to a shift of finite type.