A remark on banks theorem. Issue 11 (2nd November 2018)

• Record Type: Journal Article
• Authors: Yang, Chengyu; Li, Zhiming
• Is Part Of: Journal of difference equations and applications. Volume 24:Issue 11(2018)
• Page Start: 1777
• Page End: 1782
• Publication Date: 2018-11-02
• Subjects: Non-autonomous dynamical system -- topological transitivity -- sensitive dependence on initial condition -- Banks et al. Theorem; 58F11 -- 58F15; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2018.1543413
• Languages: English
• ISSNs: 1023-6198

Abstract

ABSTRACT: For discrete autonomous dynamical systems, it was found that in the three conditions defining Devaney chaos, topological transitivity and dense periodic points together imply sensitive dependence on initial condition (Banks, Brooks, Cairns, Davis and Stacey, On Devaney's definition of chaos, The Amer. Math. Monthly 99 (1992), pp. 332–334). In this paper, we give the definition of finitely generated non-autonomous dynamical systems (NADS) and generalize the Banks et al. theorem to the finitely generated NADS.