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In this paper we study the large deviation property for chaotic binary sequences generated by one-dimensional maps displaying chaos and thresholds functions. We deal with the case when nonlinear maps are the r-adic maps. The large deviation theory for dynamical systems is useful for investigating this problem.
There are several attempts to generate chaotic binary sequences by using one-dimensional maps. From the standpoint of engineering applications, it is necessary to evaluate statistical properties of sample sequences of finite length. In this paper we attempt to evaluate the statistics of chaotic binary sequences of finite length. The large deviation theory for dynamical systems is useful for investigating this problem.