Acta Mathematicae Applicatae Sinica, 24, 547–553 (2001)įalconer, K. Jia, B.: The Hausdorff measure of sets of finite type of one-sided symbolic space (in Chinese). Zhou, Z., Jia, B.: Hausdorff measure of sets of finite type of one-sided symbolic space. Kenyon, R., Peres, Y.: Intersecting random translates of invariant Cantor sets. Walters, P.: An Introduction to Ergodic Theory, Springer-Verlag, New York, 1982 Strong Mixing Subshift of Finite Type and Hausdorff Measure of Its Chaotic Set 0 Authors, Song, Wan Gan Hu, Zhi Wu, Hua Ming Affiliation, Peking Univ. As a measurement of chaos, we say that a map f for which htop(f) > 0 is chaotic. Chaos, Solitons and Fractals, 30, 859–863 (2006) We focus on symbolic dynamics in the form of subshifts of finite type. Wang, H., Song, W.: The Hausdorff measure of chaotic sets of adjoint shift maps. Wang, H., Xiong, J.: Chaos for subshifts of finite type. Xiong, J., Chen, E.: Chaos caused by a strong-mixing measure-preserving transformation. Xiong, J.: Hausdorff dimension of a chaotic set of shift of symbolic space. In mathematics, subshifts of finite type are used to model dynamical systems, and in particular are the objects of study in symbolic dynamics and ergodic. ed.), World Scientific, Singapore, New York, 1992, 550–572 In: Dynamical Systems ands Related Topics (Shiraiwa, K. Xiong, J, Yang, Z.: Chaos caused by a topologically mixing map. Li, T., Yorke, J.: Period 3 implies chaos. Providence: American Mathematical Society. Using an entropy addition formula derived from this formalism we prove that whenever is finitely. We introduce the notion of group charts, which gives us a tool to embed an arbitrary -subshift into a -subshift. These subshifts are the orbit closures of certain nonperiodic recurrent points of a shift map. On the entropies of subshifts of finite type on countable amenable groups. Ordinary Differential Equations and Dynamical Systems. The chaotic properties of some subshift maps are investigated. This paper deals with chaos for subshifts of finite type. An introduction to symbolic dynamics and coding. ISBN 0-19-853390-X (Provides a short expository introduction, with exercises, and extensive references.) (2)When F f11g, X(F) is a shift of nite type called the golden mean shift. Some examples (and non-examples): (1)The full shift is a shift of nite type, corresponding to F. Keane, Ergodic theory and subshifts of finite type, (1991), appearing as Chapter 2 in Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Tim Bedford, Michael Keane and Caroline Series, Eds. A subshift X Q n2Z Ais called a subshift of nite type (or usually just a shift of nite type) if there exists a nite set of words Fsuch that X X(F). Natasha Jonoska, Subshifts of Finite Type, Sofic Systems and Graphs, (2000).Substitutions in dynamics, arithmetics and combinatorics. Berthé, Valérie Ferenczi, Sébastien Mauduit, Christian et al. David Damanik, Strictly Ergodic Subshifts and Associated Operators, (2005).Introduction to Dynamical Systems (2nd ed.). A class of symbolic dynamical system, i.e., subshift of finite type symbolic dynamical system is considered in this paper. Matthew Nicol and Karl Petersen, (2009) " Ergodic Theory: Basic Examples and Constructions",Įncyclopedia of Complexity and Systems Science, Springer
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