Invariance of multivariate Li-Yorke chaos

In this paper, the invariance of multivariate Li-Yorke chaos is mainly investigated in non-autonomous discrete systems. It is shown that Li-Yorke <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -chaos implies Li-Yorke <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m"> <mml:semantics> <mml:mi>m</mml:mi> <mml:annotation encoding="application/x-tex">m</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -chaos for any <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="2 less-than-or-equal-to m greater-than n"> <mml:semantics> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo> ≤ </mml:mo> <mml:mi>m</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">2\leq m&gt; n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , while the converse is not true. Under certain conditions, it is obtained that the non-emptiness of the Li-Yorke <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="m"> <mml:semantics> <mml:mi>m</mml:mi> <mml:annotation encoding="application/x-tex">m</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -scrambled set implies the non-emptiness of the Li-Yorke <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n"> <mml:semantics> <mml:mi>n</mml:mi> <mml:annotation encoding="application/x-tex">n</mml:annotation> </mml:semantics> </mml:math> </inline-formula> -scrambled set for any <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="n greater-than m"> <mml:semantics> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>&gt;</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">n&gt; m</mml:annotation> </mml:semantics> </mml:math> </inline-formula> . 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.