Answering two open problems on Banks theorem for non-autonomous dynamical systems. Issue 12 (2nd December 2019)

• Record Type: Journal Article
• Authors: Wu, Xinxing; Chen, Guanrong
• Is Part Of: Journal of difference equations and applications. Volume 25:Issue 12(2019)
• Page Start: 1790
• Page End: 1794
• Publication Date: 2019-12-02
• Subjects: Non-autonomous dynamical system (NADS) -- topological transitivity -- Banks theorem -- Thue-Morse sequence; 54H20 -- 37B55; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2019.1696324
• Languages: English
• ISSNs: 1023-6198

Abstract

ABSTRACT: This paper shows that (1) there exists a topologically transitive NADS having two disjoint invariant periodic orbits with dense periodic points, which is finitely generated but not periodic; (2) there exists a topologically transitive non-finitely generated NADS having two disjoint invariant periodic orbits with dense periodic points, which is not sensitive. This answers positively the Open Problems 4.1 and 4.2 posed in Yang and Li [ A remark on Banks theorem, J. Difference Equ. Appl. 24 (2018), pp. 1777–1782].