SUBSHIFTS OF FINITE TYPE WITH A HOLE

We consider a subshift of finite type on q symbols with a union of t cylinders based at words of identical length p as the hole. We explore the relationship between the escape rate into the hole and a rational function, r(z), of correlations between forbidden words in the subshift with the hole. In particular, we prove that there exists a constant D(t, p) such that if q > D(t, p), then the escape rate is faster into the hole when the value of the corresponding rational function r(z) evaluated at D(t, p) is larger. Further, we consider holes which are unions of cylinders based at words of identical length, having zero cross-correlations, and prove that the escape rate is faster into the hole with larger Poincare recurrence time. Our results are more general than the existing ones known for maps conjugate to a full shift with a single cylinder as the hole.