Is the center manifold theorem applicable if say for a planar (2D) system of non-linear ODE, the stability matrix has both eigenvalues zero? Of course, there is only one eigenvector.
If not, what is the way to approach such a problem?
$\begingroup$
$\endgroup$
1
-
5$\begingroup$ Of course the center manifold theorem is applicable to this case. It just does not reduce the system beyond what it is. $\endgroup$– Michael RenardyJul 19, 2018 at 16:31
Add a comment
|
1 Answer
$\begingroup$
$\endgroup$
Yes, with a two dimensional center manifold. If you have a planar system with an equilibrium at which the Jacobian has two zero eigenvalues but only one linearly independent eigenvector, then you may have a Bogdanov-Takens (double-zero bifurcation) in your system.
