Demonstrates invariance of Li-Yorke chaos in non-autonomous discrete systems, suggesting implications for chaos theory.
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≤ 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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Pi et al. (2026) studied this question.
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