Coding nested mixing one-sided subshifts of finite type as Markov shifts having exactly the same alphabet
Alejandro Maass, Servet Martı́nez · Proceedings of the American Mathematical Society · 1998
Let X 0 X_{0} , X X be mixing one-sided subshifts of finite type such that X 0 ⊆ X X_{0}\subseteq X . We show a necessary and sufficient condition for the existence of mixing Markov shifts Y 0 Y_{0} , Y Y , Y 0 ⊆ Y Y_{0}\subseteq Y , and a conjugacy π : Y → X \pi : Y\to X with π ( Y 0 ) = X 0 \pi (Y_{0})=X_{0} , such that the sets of letters appearing in both systems are the same, more precisely, L 1 ( Y 0 ) = L 1 ( Y ) L_{1}(Y_{0})=L_{1}(Y) .