  We showed that for any bounded neighborhood of a hyperbolic equilibrium point
$x_0$, there is a transformation which is locally homeomorphism, such that the
system is changed into a linear system in this neighborhood.
  If the eigenvalues of $Df(x_0)$ are all located in the left-half complex
plane, then there is a homeomorphism on the whole region of attraction such
that the nonlinear system on the region of attraction is changed into a linear
system under such a coordinate change.
