Statistic Character in Nonlinear Systems

The statistic character in nonlinear systems will be clarified in this paper. The distributions of frequency, inter-occurrence times, first passage time and visitation density in unimodal surjective map and Lorenz type maps are discussed carefully. These two kinds of nonlinear systems have same distributions, which are explained in theory. One also elicits catholicity of the statistic character. In the field of application, we hope to afford a symbolic platform which satisfies these statistic character and study some properties of DNA sequences, 20 amino acids symbolic sequences of protein structure, and the time series that can be symbolic in finance market et al.