Let $X$ and $Y$ be $C^1$ vector feilds on $R^m$. Suppose that $0$ is an attracting hyperbolic singularity for $X$ and $Y$. Show that there exists a homemorphism $h$ of a neighborhood of origin which conjugate the diffeomorphisms $X1$ and $Y1$ but does not take orbits of $X$ to orbits of $Y$.
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$\begingroup$ Looks like homework to me... $\endgroup$– Loïc TeyssierCommented Jun 22, 2015 at 17:16
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$\begingroup$ i see Stability of singularity in singular holomorphic foliation but i think different by my questions $\endgroup$– rezaCommented Jun 23, 2015 at 11:09
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