A NOTE ON THE RETURN TIME OF STURMIAN SEQUENCES

  • Kim, Dong Han (Department of Mathematics, The University of Suwon)
  • Received : 2008.06.16
  • Published : 2008.09.30

Abstract

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 $1/{\beta}$.

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Acknowledgement

Supported by : Korea Research Foundation