I have several questions regarding some concepts of dynamic system.
1. A dynamic system is hyperbolic if all of the eigenvalue of Df(a) have non-zero real point
Does it mean that the DS(dynamic system) is hyperbolic when the eigenvalue is strictly non-zero and real? or is it also hyperbolic if the real parts of eigenvalues are non zero. when the eigenvelues includes some imaginary parts and real parts?
2. Stability of equilibrium points.
I found equilibrium points and processed it through jacobian matrix, so I have found some eigenvalues of jacobian matrix for each equilibrium points. now I want to state the stability of equilibrium points but I do not know how to determine if it is stable or unstable or center manifold. How can I find out the stability?