Conditions for maps to be topologically conjugate or semi-conjugate to subshifts of finite type and criteria of chaos. Issue 4 (1st October 2016)

• Record Type: Journal Article
• Authors: Ju, Hyonhui; Shao, Hua; Choe, Yunmi; Shi, Yuming
• Is Part Of: Dynamical systems. Volume 31:Issue 4(2016)
• Page Start: 496
• Page End: 505
• Publication Date: 2016-10-01
• Subjects: Topological conjugacy -- topological semi-conjugacy -- symbolic dynamical system -- Li-Yorke chaos -- coupled-expansion; 2010 AMS Classification 37C15 -- 37B10 -- 37D45; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2016.1158240
• Languages: English
• ISSNs: 1468-9367

Abstract

ABSTRACT: In this paper, some necessary and sufficient conditions are given for maps in Hausdorff spaces to be topologically conjugate or semi-conjugate to subshifts of finite type. These results not only extend some related existing results in metric spaces to Hausdorff spaces but also relax their conditions. In addition, it is shown that the strict A -coupled-expansion for a map in a Hausdorff space is a sufficient condition for it to be semi-conjugate to the subshift σ A in Σ + m ( A ). Based on these results, two new criteria of chaos are established, in which the maps are shown to be chaotic either in the sense of both Devaney and Li-Yorke or in the sense of Li-Yorke.