Hi all, I am not familiar with the dynamic system theory. When I was trying to understand the weakly nonlinear stability analysis, I realize the following question. It is known that the center manifold reduction can be used to study the first linear bifurcation. This lead to the Ginzburg-Landau equation Is the center manifold corresponding to the space ? I feel this because at the linear bifurcation, the growth rate of the disturbance is zero, which implies that in the above equation. Then does there exist a submanifold corresponding to ? Thanks a lot.