Work

Li-Yorke chaos on fuzzy dynamical systems

Year: 2026

Type: article

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.

Source: Information Sciences

DOI: 10.1016/j.ins.2026.123527

Authors: Illych Alvarez, Antoni López-Martínez

Institutions: Escuela Superior Politecnica del Litoral, Universitat Politècnica de València

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,200

Funder: Ministerio de Ciencia, Innovación y Universidades