Xiong chaos for set-valued dynamical systems
Abstract
Let (X,F) be a set-valued dynamical system, where X is a compact metric space and F:Xto 2^Xsetminus∅is a set-valued map. We introduce the notions of Xiong chaos, strong Xiong chaos, weak mixing, and distributional chaos for set-valued dynamical systems. We show that Xiong chaos and weak mixing are equivalent, and that strong Xiong chaos sets are distributional chaos in a sequence.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Advanced Topology and Set Theory
Chaos control and synchronization
Publication details
- Journal / source
- Scientia Sinica Mathematica
- Publication date
- 1 January 2026
- Language
- EN