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March 31st, 2015, 06:08 AM  #1 
Newbie Joined: Jun 2013 Posts: 1 Thanks: 0  Topology equivalence in dynamical system
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. 

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dynamical, equivalence, system, topology 
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