• 대한수학회논문집
• /
• 제8권4호
• /
• pp.655-668
• /
• 1993

• Korean Journal of Mathematics
• /
• 제16권3호
• /
• pp.301-307
• /
• 2008

Let $R_n$ be the the first return time to its initial n-word. Then the Ornstein-Weiss first return time theorem implies that log$R_n$ divided by n converges to entropy. We consider the convergence of log$R_n$ 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 $1{\leq}{\alpha},\;{\beta}{\leq}{\infty}$, there is a Sturmian sequence of which limsup is ${\alpha}$ and liminf is $1/{\beta}$.