Invariance of multivariate Li-Yorke chaos

Jingmin Pi; Qigui Yang

doi:10.1090/proc/17556

journal article Mar 11, 2026

Invariance of multivariate Li-Yorke chaos

Jingmin Pi Qigui Yang

Proceedings of the American Mathematical Society Vol. 154 No. 5 pp. 2019-2033 · American Mathematical Society (AMS)

View at Publisher Save 10.1090/proc/17556

Abstract

In this paper, the invariance of multivariate Li-Yorke chaos is mainly investigated in non-autonomous discrete systems. It is shown that Li-Yorke

n
n

-chaos implies Li-Yorke

m
m

-chaos for any

2

≤

m
>
n

2\leq m> n

, while the converse is not true. Under certain conditions, it is obtained that the non-emptiness of the Li-Yorke

m
m

-scrambled set implies the non-emptiness of the Li-Yorke

n
n

-scrambled set for any

n
>
m

n> m

. Furthermore, it is illustrated that multivariate Li-Yorke chaos remains invariant under topological conjugation. Subsequently, it is demonstrated that in uniformly convergent non-autonomous discrete systems, multivariate Li-Yorke chaos remains invariant under iteration. Moreover, it is shown that multivariate Li-Yorke chaos can be preserved under the product operation.

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Published: Mar 11, 2026
Vol/Issue: 154(5)
Pages: 2019-2033
License: View

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Cite This Article

Jingmin Pi, Qigui Yang (2026). Invariance of multivariate Li-Yorke chaos. Proceedings of the American Mathematical Society, 154(5), 2019-2033. https://doi.org/10.1090/proc/17556

Invariance of multivariate Li-Yorke chaos

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