Chaotic properties of subshifts generated by a nonperiodic recurrent orbit

The chaotic properties of some subshift maps are investigated. These subshi fts are the orbit closures of certain nonperiodic recurrent points of a shi ft map. We first provide a review of basic concepts for dynamics of continu ous maps in metric spaces. These concepts include nonwandering point, recur rent Feint, eventually periodic point, scrambled set, sensitive dependence on initial conditions, Robinson chaos, and topological entropy. Next we rev iew 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 se nse of Robinson. Moreover, we show that such a subshift has an infinite scr ambled set if it has a periodic point. Finally, we give some examples and d iscuss the topological entropy of these subshifts, and present two open pro blems on the dynamics of subshifts.