Geodesic
Positive entropy implies chaos along any infinite sequence
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 82 (2021) no. 1, pp. 3-18.

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Let $G$ be an infinite countable discrete amenable group. For any $G$-action on a compact metric space $(X,\rho)$, it turns out that if the action has positive topological entropy, then for any sequence $\{s_i\}_{i=1}^{+\infty}$ with pairwise distinct elements in $G$ there exists a Cantor subset $K$ of $X$ which is Li–Yorke chaotic along this sequence, that is, for any two distinct points $x,y\in K$, one has $$ \limsup\limits_{i\to+\infty}\rho(s_i x,s_iy)>0,\ \text{and}\ \liminf_{i\to+\infty}\rho(s_ix,s_iy)=0. $$ 
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Wen Huang; Jian Li; Xiangdong Ye. Positive entropy implies chaos along any infinite sequence. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 82 (2021) no. 1, pp. 3-18. http://geodesic.mathdoc.fr/item/MMO_2021_82_1_a0/

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