\begin{tikzpicture}

% draw axis
\draw[thick, ->] (-0.5cm, 0cm) -- (5cm, 0cm) node[anchor=south] {$\Re \upomega$};
\draw[thick, ->] (0cm, -1cm) -- (0cm, 3cm) node[anchor=east] {$\Im \upomega$};

% draw branching cuts
\filldraw[fill=black!30, draw=black, dashed] (0cm, 2pt) rectangle (4.8cm, -2pt);
\filldraw[fill=black!10, draw=black, dashed] (1cm, 1pt) rectangle (4.8cm, -1pt);

% draw branching points
\filldraw[fill=white, draw=black] (4.8cm, 0cm) circle (2pt) node[anchor=north] (x1) {$\infty$};
\filldraw[fill=white, draw=black] (1cm, 0cm) circle (2pt) node[anchor=north] (x2) {$1$};
\filldraw[fill=white, draw=black] (0cm, 0cm) circle (2pt) node[anchor=north east] (x3) {$0$};

\end{tikzpicture}

% vim: ft=tex