1999/10/03 by Xinchu Fu, Xin-Chu Fu, Yibin Fu +2
Computer Science · Mathematics · Physics and Astronomy · #Artificial intelligence #Cellular Automata and Applications #Chaos control and synchronization #Chaotic #Computer science #Entropy (arrow of time) #Geometry #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Metric space #Orbit (dynamics) #Periodic orbits #Periodic point #Physics #Point (geometry) #Pure mathematics #Set (abstract data type) #Subshift of finite type #Symbolic dynamics #Topological entropy #chao-dyn #nlin.CD
paper · pdf · doi:10.1142/s021812740000075x
published as International J. Bifurcation and Chaos, Vol 10, No.5, 2000
arxiv created 1999/10/03 · openalex publication_date 2000/05/01 · arxiv updated 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The chaotic properties of some subshift maps are investigated. These subshifts are the orbit closures of certain nonperiodic recurrent points of a shift map. We first provide a review of basic concepts for dynamics of continuous maps in metric spaces. These concepts include nonwandering point, recurrent point, eventually periodic point, scrambled set, sensitive dependence on initial conditions, Robinson chaos, and topological entropy. Next we review the notion of shift maps and subshifts. Then we show that the one-sided subshifts generated by a nonperiodic recurrent point are chaotic in the sense of Robinson. Moreover, we show that such a subshift has an infinite scrambled set if it has a periodic point. Finally, we give some examples and discuss the topological entropy of these subshifts, and present two open problems on the dynamics of subshifts.