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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.

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# Center manifold and submanifold

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