Li-Yorke Sensitivity

Author

Ethan Akin, Missouri University of Science and TechnologyFollow
Sergiǐ Kolyada

Abstract

We introduce and study a concept which links the Li-Yorke versions of chaos with the notion of sensitivity to initial conditions. We say that a dynamical system (X, T) is Li-Yorke sensitive if there exists a positive ε such that every x ∈ X is a limit of points y ∈ X such that the pair (x, y) is proximal but not ε-asymptotic, i.e. for infinitely many positive integers i the distance ρ(Tⁱ(x), Tⁱ(y))is greater than ε but for any positive δ this distance is less than δ for infinitely many i.

Recommended Citation

E. Akin and S. Kolyada, "Li-Yorke Sensitivity," Nonlinearity, vol. 16, no. 4, pp. 1421 - 1433, IOP Publishing; London Mathematical Society, Jul 2003.

The definitive version is available at https://doi.org/10.1088/0951-7715/16/4/313

Department(s)

Mathematics and Statistics

International Standard Serial Number (ISSN)

0951-7715

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2026 IOP Publishing; London Mathematical Society, All rights reserved.

Publication Date

01 Jul 2003