English

Devaney chaos of multiple mappings from a set-valued view

Dynamical Systems 2023-11-08 v1

Abstract

In this paper, we introduce the definitions of periodic point, transitivity, sensitivity and Devaney chaos of multiple mappings from a set-valued perspective. We study the relation between multiple mappings and its continuous self-maps and show that multiple mappings and its continuous self-maps do not imply each other in terms of periodic point or transitivity. While the sufficient condition for multiple mappings to have periodic points, to be transitive and sensitive is provided separately. And we show that transitivity plus dense periodic point set implies sensitivity. Also, a sufficient condition for multiple mappings to be Devaney chaotic is given.

Keywords

Cite

@article{arxiv.2311.03715,
  title  = {Devaney chaos of multiple mappings from a set-valued view},
  author = {Yingcui Zhao},
  journal= {arXiv preprint arXiv:2311.03715},
  year   = {2023}
}

Comments

arXiv admin note: substantial text overlap with arXiv:2311.02932

R2 v1 2026-06-28T13:13:35.795Z