  If a topological dynamical system $(X,T)$ has positive topological entropy,
then it is multivariant mean Li-Yorke chaotic along a sequence
$\{a_k\}_{k=1}^\infty$ of positive integers which is "good" for pointwise
ergodic convergence with a mild condition; more specifically, there exists a
Cantor subset $K$ of $X$ such that for every $n\ge2$ and pairwise distinct
points $x_1,x_2,\dotsc,x_n$ in $K$ we have
\[\liminf_{N\to\infty}\frac{1}{N}\sum_{k=1}^N\max_{1\leq i<j\leq n}
d(T^{a_k}x_i,T^{a_k}x_j)=0\] and
\[\limsup_{N\to\infty}\frac{1}{N}\sum_{k=1}^N\min_{1\leq i<j\leq n}
d(T^{a_k}x_i,T^{a_k}x_j)>0.\] Examples are given for the classic sequences of
primes and generalized polynomials.
