Topology equivalence in dynamical system

Jun 2010
31
0
Bandung
Hi, my name is Eric.

I've got trouble when proofing that system
\(\displaystyle \dot{x}=\alpha+x^2+O(x^3)\) is topological equivalence with system \(\displaystyle \dot{x}=\alpha+x^2\).
I don't understand how to build the homeomorphism for the orbit.
In literature, I read that for \(\displaystyle \alpha>0\), the homeomorphism mapping is defined by \(\displaystyle h_\alpha(x)=x\), whereas when \(\displaystyle \alpha<0\) define \(\displaystyle h_\alpha(x)=a(\alpha)+b(\alpha)x\).

What is the function \(\displaystyle a(\alpha) \text{ }b(\alpha)\) explicitly?
Could someone please help me?
Thank you so much.(Bow)
 
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