Work

Δ-weak mixing and asynchronous Li-Yorke chaos

Year: 2026

Type: article

Abstract: In this paper, we investigate Δ-weakly mixing sets and asynchronous Li–Yorke chaos. First, we prove that in a measure-theoretic sense, every ergodic, non-distal measure preserving system contains many Δ-weakly mixing subsets. Second, we show that every non-trivial transitive system contains an uncountable ( r , s ) -scrambled set for each pair of distinct r , s ∈ N ; under the stronger assumption of total transitivity, there exists a Mycielski subset that is ( r , s ) -scrambled simultaneously for all distinct r , s ∈ N .

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2026.114225

Authors: Chunlin Liu, Rongzhong Xiao, Leiye Xu, Xiaomin Zhou

Institutions: Dalian University of Technology, Institute of Mathematics, Polish Academy of Sciences, University of Science and Technology of China, Huazhong University of Science and Technology

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: National Natural Science Foundation of China, China Postdoctoral Science Foundation, National Key Research and Development Program of China