Boundaries of markov partitions

The core of a Markov partition is the nonwandering set of the map restricted to the boundary of the partition. We show that the core of a Markov partition is always a finitely presented system. Then we show that every one sided sofic system occurs as the core of a Markov partition for an n-fold covering map on the circle and every two sided sofic system occurs as the core of a Markov partition for a hyperbolic automorphism of the two dimensional torus. © 1992 American Mathematical Society.