Skip to main content

two vector feilds are cojugate but not take orbits

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 neighbourhood of origin which conjugate the diffmorphisms $X1$ and $Y1$ but does not take orbits of $X$ to orbits of $Y$

reza
  • 9
  • 6