Multiple equations with a large "{" in front: alignment and labelling

Instead of inserting a row that starts with three horizontal dots, you could also create a row with a set of vertical dots centered on the = signs. The code below implements this idea via the \vdotswithin macro of the mathtools package.

\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{equation}
    \begin{cases}
       \begin{aligned}
          \dot {x}_1 &= f_1(x_1,\dots,x_n) \\
          &\vdotswithin{=} \\  % vertical dots, centered on the "=" signs
          \dot {x}_n &= f_n(x_1,\dots,x_n)
       \end{aligned} 
    \end{cases}
\end{equation}
\end{document}

Try with this code:

\documentclass{minimal}
\usepackage{amsmath}
\begin{document}

\begin{equation}
    \begin{cases}
        \dot {x}_1 = f_1(x_1,\dots,x_n) \\
        \ldots \\
        \dot {x}_n = f_n(x_1,\dots,x_n)
    \end{cases}
\end{equation}

\end{document}

You can also use your code, but with some changes (which egreg said):

\begin{equation}
    \begin{cases}
        \begin{array}{lr}
            \dot {x}_1 = f_1(x_1,\dots,x_n) \\
            \hspace{13pt}   \dots \\
            \dot {x}_n = f_n(x_1,\dots,x_n)  \\
        \end{array}
    \end{cases}
\end{equation}