On entropies of block-gluing subshifts

Abstract

A subshift X is called c-block gluing if for any integer n ≥ c and any two blocks u and v from the language of X there exists an element of X which has occurrences of u and v at distance n. In this note we study the topological entropies of c-block gluing binary onedimensional subshifts. We define the set R c to be the set of entropies of all c-block-gluing subshifts, and R = ∪ c∈N R c . We show that the set R is dense, while R 1 and R 2 are not; in particular, they have isolated points. We conjecture that the same holds for any c.