Let
G
G
be an infinite countable discrete amenable group. For any
G
G
-action on a compact metric space
(
X
,
ρ
)
(X,\rho )
, it turns out that if the action has positive topological entropy, then for any sequence
{
s
i
}
i
=
1
+
∞
\{s_i\}_{i=1}^{+\infty }
with pairwise distinct elements in
G
G
there exists a Cantor subset
K
K
of
X
X
which is Li–Yorke chaotic along this sequence, that is, for any two distinct points
x
,
y
∈
K
x,y\in K
, one has
\[
lim sup
i
→
+
∞
ρ
(
s
i
x
,
s
i
y
)
>
0
and
lim inf
i
→
+
∞
ρ
(
s
i
x
,
s
i
y
)
=
0.
\limsup _{i\to +\infty }\rho (s_i x,s_iy)>0\ \text {and}\ \liminf _{i\to +\infty }\rho (s_ix,s_iy)=0.
\]