Let $X=\left\{0,1,2\right\}^{\mathbb{Z}}$ and on it the following dynamics described by $T\colon X\to X$ as follows: A 1 becomes a 2, a 2 becomes a 0 and a 0 becomes a 1 if at least one of its two neighbors is 1.
Moreover, consider $$ Y=\bigcap_{n=1}^{\infty}T^n(X). $$
Show that for the Topological Entropy of $T$ it is $$ h(X,T)=h(Y,T). $$
Edit
"$\leqslant$": Because $Y\subset X$ is closed and $T(Y)=Y$, it is $h(Y,T)\leqslant h(X,T)$.
"$\geqslant$": How to show this?
Edit: Already found an answer by myself.