A NOTE ON THE RETURN TIME OF STURMIAN SEQUENCES
Donghan Kim · Korean Journal of Mathematics · 2008
Let be the the first return time to its initial n-word. Then the Ornstein-Weiss first return time theorem implies that log divided by n converges to entropy. We consider the convergence of log for Sturmian sequences which has the lowest complexity. In this case, we normalize the logarithm of the first return time by log n. We show that for any numbers , there is a Sturmian sequence of which limsup is and liminf is .