I am studying a dynamical system which has an equilibrium point where the linearisation of the system at that point exhibits one eigenvalue which is exactly 0. According to Wikipedia that means that the corresponding eigenvector spans a slow manifold, correct?
To my understanding a slow manifold is a special case of a centre manifold – the case when not only the real part of the eigenvalue is zero, but also the imaginary part.
Are there any special techniques to analyse the stability of this equilibrium point, or are those the same than for centre manifolds? Can anyone recommend a good book or online source on the topic?
In particular I am also interested at the question why a slow manifold is called slow? Is it because solutions approach or get repelled from the fixed point at a slow rate?
Cheers for explanations!