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 Differential Equations Ordinary and Partial Differential Equations Math Forum

 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. Tags dynamical, equivalence, system, topology Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post vercammen Topology 1 October 19th, 2012 11:06 AM 3,14oner Applied Math 0 April 7th, 2012 02:36 AM agsmith87 Real Analysis 0 February 9th, 2012 08:02 PM genoatopologist Topology 0 December 6th, 2008 10:09 AM Erdos32212 Topology 0 December 2nd, 2008 01:04 PM

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