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

Let's consider the system:

<br />
\dot{x}=\mu+x^2-xy
\dot{y}=y^2-x^2-1<br />

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

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