Theorem 5.4.4
Suppose that \(f\) has the form
\begin{equation*}
f(z) = z + a z^{n+1} + O(z^{n+2}).
\end{equation*}
Then zero is a fixed, parabolic point in the Fatou set of \(f\text{.}\) Suppose also that \(v\) is a solution of
\begin{equation*}
nav^n=1.
\end{equation*}
Then, \(f\) is repulsive in the direction \(v\text{.}\) Suppose, on the other hand that \(v\) is a solution of
\begin{equation*}
nav^n=-1.
\end{equation*}
Then, \(f\) is attractive in the direction \(v\text{.}\)