On the entropy of \(\mathbb{Z}^d\) subshifts of finite type (Q676028)

Using matrix representations of higher-dimensional subshifts of finite type, it is shown that the ``combinatorial'' entropy (the growth in the number of finite words) coincides with the topological entropy. Conditions are given under which the growth rate of periodic points coincides with the topological entropy. As is well known, this gives a convergent sequence of numbers, each readily computable, whose limit is the topological entropy and whose rate of convergence may be estimated. In a more restrictive setting, this has been used by \textit{N. G. Markley and M. E. Paul} [Proc. Lond. Math. Soc., III. Ser. 43, 251-272 (1981; Zbl 0479.54022); Lect. Notes Pure Appl. Math. 70, 135-157 (1981; Zbl 0475.58010)].