Multi-transitivity of semigroup actions. Issue 9 (2nd September 2021)

• Record Type: Journal Article
• Authors: Wang, Huoyun; Fang, Junyan; Zhong, Xinlin
• Is Part Of: Journal of difference equations and applications. Volume 27:Issue 9(2021)
• Page Start: 1263
• Page End: 1279
• Publication Date: 2021-09-02
• Subjects: Multi-transitivity -- Δ-transitivity -- semigroup action -- Li–Yorke chaos; Primary: 37C50 -- Secondary: 37C15; Difference equations -- Periodicals; 515.625
• DOI: 10.1080/10236198.2021.1985483
• Languages: English
• ISSNs: 1023-6198

Abstract

Abstract : Moothathu [Colloq. Math. 120 (2010), pp. 127–138] proved that multi-transitivity, weakly mixing and Δ-transitivity are equivalent for minimal homeomorphisms. In this paper, we extend this result to Abelian group actions. Moreover, we point out that a multi-transitive system of Abelian group action is Li–Yorke ε -chaotic for some ε > 0 .