  For any $\beta > 1$, let $T_\beta: [0,1)\rightarrow [0,1)$ be the
$\beta$-transformation defined by $T_\beta x=\beta x \mod 1$. We study the
uniform recurrence properties of the orbit of a point under the
$\beta$-transformation to the point itself. The size of the set of points with
prescribed uniform recurrence rate is obtained. More precisely, for any $0\leq
\hat{r}\leq +\infty$, the set $$\left\{x \in [0,1): \forall\ N\gg1, \exists\
1\leq n \leq N, {\rm\ s.t.}\ |T^n_\beta x-x|\leq \beta^{-\hat{r}N}\right\}$$ is
of Hausdorff dimension $\left(\frac{1-\hat{r}}{1+\hat{r}}\right)^2$ if $0\leq
\hat{r}\leq 1$ and is countable if $\hat{r}>1$.
