Li-Yorke chaos on fuzzy dynamical systems
arXiv:2510.20240 · doi:10.1016/j.ins.2026.123527
The paper examines how various forms of Li‑Yorke chaos are preserved when a dynamical system is extended to the space of compact subsets and to the space of normal fuzzy subsets, proving one‑way transfer results and introducing a stronger Cantor‑dense Li‑Yorke chaos that can transfer back under certain conditions.
Abstract
Given a dynamical system we investigate how several variants of Li-Yorke chaos behave with respect to the extended systems and , where is the hyperextension of acting on the space of non-empty compact subsets of , and where denotes the Zadeh extension of acting on the space of normal fuzzy subsets of . We first prove that the main variants of Li-Yorke chaos transfer from to and from to , but that the converse implications do not hold in general. However, combining the notions of proximality and sensitivity we introduce Cantor-dense Li-Yorke chaos, and we prove that this strengthened variant of chaos does transfer from to under natural assumptions.
32 pages