2022/09/29 by Yingcui Zhao, Zhao, Yingcui
Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2210.07944
openalex publication_date 2022/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce the definition of Li-Yorke chaos for the map f on G-spaces, and show G-Li-Yorke chaos is iterable for f. Li-Yorke chaos implies G-Li-Yorke chaos, while the converse is not true. Then we give a sufficient condition for f to be chaotic in the sense of G-Li-Yorke. Also, we prove that if f is G-transitive and there exists a common fixed point for f and all of the maps in G, then f is chaotic in the sense of G-Li-Yorke.