I consider a topological dynamical system $(X,S)$, where $X$ is a product space $\{0,1\}^{\mathbb{Z}}$ and $S:X\to X$ is a shift map, i.e. $S((x_n)_{n\in\mathbb{Z}})=(y_n)_{n\in\mathbb{Z}}, y_n=x_{n+1}$ for all $n\in\mathbb{Z}$. Then we consider some subshifts, $(Y,S), Y\subset X$, $Y$ is closed and $S$-invariant. And my question is, how can I prove that subshifts always have at least one measure of maximal entropy? I found somewhere this fact but I cannot prove it. And I found that is for example a $(\frac{1}{2},\frac{1}{2})$-Bernoulli measure. How looks some other measures of maximal entropy? In general how can I discribe these measures? When there exists only one measure of maximal entropy? I know that then the system is called an intrisically ergodic.
Ok, so thank you in advance for any tips and help.