# Taylor Perturbation

• January 24th 2011, 05:13 AM
Dinkydoe
Taylor Perturbation
Hi, I'm not sure what to do with this...

Let's consider the system:

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

$\dot{y}=y^2-x^2-1
$

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 $\mu$)