Li-Yorke chaos for maps on G-Spaces

Abstract

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.