my name is Eric.
I've got trouble when proofing that system $\dot{x}=\alpha+x^2+O(x^3)$ is topological equivalence with system $\dot{x}=\alpha+x^2$. I don't understand how to build the homeomorphism for the orbit. In literature, I read that for $\alpha>0$, the homeomorphism mapping is defined by $h_\alpha(x)=x$, whereas when $\alpha<0$ define $h_\alpha(x)=a(\alpha)+b(\alpha)x$.
What is the function $a(\alpha) \text{ }b(\alpha)$ explicitly? Could someone please help me? Thank you so much.(Bow)