Hi, I'm not sure what to do with this...

Let's consider the system:

$\displaystyle
\dot{x}=\mu+x^2-xy$
$\displaystyle \dot{y}=y^2-x^2-1
$

For $\displaystyle \mu=0$ we have saddles $\displaystyle P_1(0)=(1,0),P_2(0)=(-1,0)$. Now we consider $\displaystyle \mu\neq 0$ small.

How do we determine a Tayler/Pertubation-expansion of the saddles $\displaystyle P_1(\mu),P_2(\mu)$? (upto quadratic terms in $\displaystyle \mu$)