Chaotic properties of subshifts generated by a nonperiodic recurrent orbit

Citation
Xc. Fu et al., Chaotic properties of subshifts generated by a nonperiodic recurrent orbit, INT J B CH, 10(5), 2000, pp. 1067-1073
Citations number
35
Language
INGLESE
art.tipo
Article
Categorie Soggetti
Multidisciplinary
Journal title
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
ISSN journal
0218-1274 → ACNP
Volume
10
Issue
5
Year of publication
2000
Pages
1067 - 1073
Database
ISI
SICI code
0218-1274(200005)10:5<1067:CPOSGB>2.0.ZU;2-L
Abstract
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.