  We introduce subshifts of quasi-finite type as a generalization of the
well-known subshifts of finite type. This generalization is much less rigid and
therefore contains the symbolic dynamics of many non-uniform systems, e.g.,
piecewise monotonic maps of the interval with positive entropy. Yet many
properties remain: existence of finitely many ergodic invariant probabilities
of maximum entropy; lots of periodic points; meromorphic extension of the
Artin-Mazur zeta function.
