English

Li-Yorke chaos for maps on G-Spaces

Dynamical Systems 2024-09-04 v2

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.

Keywords

Cite

@article{arxiv.2210.07944,
  title  = {Li-Yorke chaos for maps on G-Spaces},
  author = {Yingcui Zhao},
  journal= {arXiv preprint arXiv:2210.07944},
  year   = {2024}
}