Multiformity of inherent randomicity and visitation density in n symbolic dynamics

The multiformity of inherent randomicity and visitation density in n symbolic dynamics will be clarified in this paper. These stochastic symbolic sequences bear three features. The distribution of frequency, inter-occurrence times and the alignment of two random sequences are amplified in detail. The features of visitation density in surjective maps presents catholicity and the catholicity in n letters randomicity has the same measure foundation. We hope to offer a symbolic platform that satisfies these stochastic properties and to attempt to study certain properties of DNA base sequences, 20 amino acids symbolic sequences of proteid structure, and the time series that can be symbolic in finance market et al.

[1]  Peng,et al.  Global metric regularity of the devil's staircase of topological entropy. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  Zhong Zhou,et al.  Entropy invariants: II. The block structure of Stefan matrices , 2003 .

[3]  K. Cao,et al.  An effective numerical method of the word-lifting technique in one-dimensional multimodal maps , 2003 .

[4]  N. Komarova,et al.  Nonlinear waves in double-stranded DNA , 2004, Bulletin of mathematical biology.

[5]  Zhong Zhou,et al.  Inherent randomicity in 4-symbolic dynamics , 2006 .

[6]  B. Hao,et al.  Fractals from genomes – exact solutions of a biology-inspired problem , 1999, cond-mat/9910422.

[7]  J. Yorke,et al.  On the existence of invariant measures for piecewise monotonic transformations , 1973 .

[8]  M. Mackey,et al.  Probabilistic properties of deterministic systems , 1985, Acta Applicandae Mathematicae.

[9]  Li-Shi Luo,et al.  The ordering of critical periodic points in coordinate space by symbolic dynamics , 1991 .

[10]  Peng,et al.  Symbolic dynamics analysis of topological entropy and its multifractal structure. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  B. Hao,et al.  Directions in chaos , 1987 .

[12]  Pierre Collet,et al.  Asymptotic limit law for the close approach of two trajectories in expanding maps of the circle , 1994 .

[13]  Patrick Billingsley,et al.  Probability and Measure. , 1986 .

[14]  Tohru Kohda,et al.  Piecewise polynomial galerkin approximation to invariant densities of one-dimensional difference equations , 1982 .

[15]  Bruce J. West,et al.  A dynamical approach to DNA sequences , 1996 .

[16]  S. Peng,et al.  Disorder versus order: global multifractal relationship between topological entropies and universal convergence rates , 1996 .

[17]  B. Hao,et al.  Fractals related to long DNA sequences and complete genomes , 2000 .

[18]  S. Razin,et al.  Mapping long-range chromatin organization within the chicken alpha-globin gene domain using oligonucleotide DNA arrays. , 2005, Genomics.

[19]  B. Hao,et al.  Symbolic dynamics and characterization of complexity , 1991 .

[20]  S. M. Ulam,et al.  On Combination of Stochastic and Deterministic Processes , 1947 .

[21]  B. Hao,et al.  Elementary Symbolic Dynamics And Chaos In Dissipative Systems , 1989 .

[22]  Jifa Jiang,et al.  On the topological entropy, nonwandering set and chaos of monotone and competitive dynamical systems , 2002 .

[23]  Cyclic star products and universalities in symbolic dynamics of trimodal maps , 2000 .

[24]  Multifractal and probabilistic properties of DNA sequences , 2001 .

[25]  J. Eckmann,et al.  Iterated maps on the interval as dynamical systems , 1980 .

[26]  J. Yorke,et al.  Period Three Implies Chaos , 1975 .

[27]  Tien Yien Li,et al.  Markov finite approximation of Frobenius-Perron operator , 1991 .

[28]  Zhong Zhou,et al.  Entropy invariants: I. The universal order relation of order-preserving star products , 2003 .

[29]  James A. Yorke,et al.  Ergodic transformations from an interval into itself , 1978 .

[30]  Shou-Li Peng,et al.  Devil's staircase of topological entropy and global metric regularity , 1994 .

[31]  Zaqueu Coelho,et al.  On discrete stochastic processes generated by deterministic sequences and multiplication machines , 2000 .

[32]  Metric universality for the devil's staircase of topological entropy , 1996 .

[33]  Tien-Yien Li.  Finite approximation for the Frobenius-Perron operator. A solution to Ulam's conjecture , 1976 .