I have a question about center spaces. Taking into account a linear differential equation we know Lyapunov theorem states: if all the eigenvalues of the matrix A have strictly negative real part then c is a stable equilibrium point for the equation. If A has at least one eigenvalue with strictly positive real part then c is an unstable equilibrium point for the equation. But the theorem does non say anything about center space. For example if I have all the eigenvalue with real part equal to zero or all negative with at least one eigenvalue with real part equal to 0 can I say something about center space or theorem simply does not apply ? Moreover If I can say something about center space how can I say if center spaces are stable or unstable ?
Thank you !